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Aufgaben:Aufgabe 2.11: Arithmetische Codierung - Versionsgeschichte
2024-03-29T07:53:36Z
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Guenter am 12. August 2021 um 12:53 Uhr
2021-08-12T12:53:03Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 12. August 2021, 12:53 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l120" >Zeile 120:</td>
<td colspan="2" class="diff-lineno">Zeile 120:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 1</u>:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 1</u>:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Aus&nbsp; $B_4 = 0.343 = B_3$&nbsp; (abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein&nbsp; $\rm X$&nbsp; war. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Aus&nbsp; $B_4 = 0.343 = B_3$&nbsp; (abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein&nbsp; $\rm X$&nbsp; war. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen.&nbsp; Man erkennt aus der Schraffierung, dass der <del class="diffchange diffchange-inline">zweite Lösungsvorschlag </del>die richtige Symbolfolge angibt: &nbsp; $\rm XXYXXXZ$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik <ins class="diffchange diffchange-inline">rechts </ins>zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen.&nbsp; </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Man erkennt aus der Schraffierung, dass der <ins class="diffchange diffchange-inline">Vorschlag 2 </ins>die richtige Symbolfolge angibt: &nbsp; $\rm XXYXXXZ$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite&nbsp; $\it \Delta$&nbsp; kann wirklich gemäß dem Vorschlag 3 ermittelt werden. Es gilt:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite&nbsp; $\it \Delta$&nbsp; kann wirklich gemäß dem Vorschlag 3 ermittelt werden. Es gilt:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm},$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm},$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$<ins class="diffchange diffchange-inline">\Rightarrow \hspace{0.3cm} </ins>{\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\hspace{0.05cm}. $$</div></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=32125&oldid=prev
Guenter am 12. August 2021 um 12:43 Uhr
2021-08-12T12:43:42Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 12. August 2021, 12:43 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11" >Zeile 11:</td>
<td colspan="2" class="diff-lineno">Zeile 11:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn&nbsp; $B$&nbsp; gehört zum Intervall&nbsp; $I$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn&nbsp; $B$&nbsp; gehört zum Intervall&nbsp; $I$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende&nbsp; $E$&nbsp; ist nicht mehr in&nbsp; $I$&nbsp; enthalten.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende&nbsp; $E$&nbsp; ist nicht mehr in&nbsp; $I$&nbsp; enthalten.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist&nbsp; ${\it} \Delta = E - B$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist&nbsp; ${\it} <ins class="diffchange diffchange-inline">{\it </ins>\Delta<ins class="diffchange diffchange-inline">} </ins>= E - B$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l23" >Zeile 23:</td>
<td colspan="2" class="diff-lineno">Zeile 23:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:} \hspace{0.25cm}0.011101\hspace{0.3cm}\Rightarrow\hspace{0.3cm}</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:} \hspace{0.25cm}0.011101<ins class="diffchange diffchange-inline">\hspace{0.05cm}\text{...}</ins>\hspace{0.3cm}\Rightarrow\hspace{0.3cm}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.25cm} \boldsymbol{\rm 011101} \hspace{0.05cm}. $$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.25cm} \boldsymbol{\rm 011101<ins class="diffchange diffchange-inline">}\hspace{0.05cm}\text{...</ins>} \hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls &nbsp;$I$, gekennzeichnet durch den Beginn &nbsp;$B$&nbsp; sowie dem Ende &nbsp;$E$&nbsp; bzw. der Breite &nbsp;$\Delta$. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls &nbsp;$I$, gekennzeichnet durch den Beginn &nbsp;$B$&nbsp; sowie dem Ende &nbsp;$E$&nbsp; bzw. der Breite &nbsp;$<ins class="diffchange diffchange-inline">{\it </ins>\Delta<ins class="diffchange diffchange-inline">}</ins>$. </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Diese Bestimmung geschieht entsprechend der Intervallschachtelung in <del class="diffchange diffchange-inline">obiger </del>Grafik. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Diese Bestimmung geschieht entsprechend der Intervallschachtelung in <ins class="diffchange diffchange-inline">nebenstehender </ins>Grafik. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen&nbsp; $\rm XXY$&nbsp; beginnt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen&nbsp; $\rm XXY$&nbsp; beginnt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l34" >Zeile 34:</td>
<td colspan="2" class="diff-lineno">Zeile 34:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.4cm}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.4cm}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.4cm} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.4cm}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.4cm}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.4cm} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist&nbsp; $\rm X$. Das bedeutet: &nbsp; das ausgewählte Intervall wird durch&nbsp; $B_0$&nbsp; und&nbsp; $C_0$&nbsp; begrenzt.&nbsp; Dieses Intervall wird mit neuem Beginn&nbsp; $B_1 = B_0$&nbsp; und neuem Ende&nbsp; $E_1 = C_0$&nbsp; in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt.&nbsp; Die Zwischenwerte sind&nbsp; $C_1$&nbsp; und&nbsp; $D_1$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist&nbsp; $\rm X$. Das bedeutet: &nbsp; das ausgewählte Intervall wird durch&nbsp; $B_0$&nbsp; und&nbsp; $C_0$&nbsp; begrenzt.&nbsp; </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Dieses Intervall wird mit neuem Beginn&nbsp; $B_1 = B_0$&nbsp; und neuem Ende&nbsp; $E_1 = C_0$&nbsp; in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt.&nbsp; Die Zwischenwerte sind&nbsp; $C_1$&nbsp; und&nbsp; $D_1$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe.&nbsp; Beispielsweise sollen in der Teilaufgabe&nbsp; '''(2)'''&nbsp; die Grenzen&nbsp; $B_2$,&nbsp; $C_2$,&nbsp; $D_2$&nbsp; und&nbsp; $E_2$&nbsp; für das zweite Symbol&nbsp; $\rm X$&nbsp; ermittelt werden und in der Teilaufgabe&nbsp; '''(3)'''&nbsp; die Grenzen&nbsp; $B_3$,&nbsp; $C_3$,&nbsp; $D_3$&nbsp; und&nbsp; $E_3$&nbsp; für das dritte Symbol&nbsp; $\rm Y$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe.&nbsp; Beispielsweise sollen in der Teilaufgabe&nbsp; '''(2)'''&nbsp; die Grenzen&nbsp; $B_2$,&nbsp; $C_2$,&nbsp; $D_2$&nbsp; und&nbsp; $E_2$&nbsp; für das zweite Symbol&nbsp; $\rm X$&nbsp; ermittelt werden und in der Teilaufgabe&nbsp; '''(3)'''&nbsp; die Grenzen&nbsp; $B_3$,&nbsp; $C_3$,&nbsp; $D_3$&nbsp; und&nbsp; $E_3$&nbsp; für das dritte Symbol&nbsp; $\rm Y$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=29400&oldid=prev
Guenter am 28. Januar 2020 um 13:13 Uhr
2020-01-28T13:13:46Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. Januar 2020, 13:13 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l105" >Zeile 105:</td>
<td colspan="2" class="diff-lineno">Zeile 105:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Auch das zweite Symbol ist $\rm X$. Bei gleichem Vorgehen wie in der Aufgabenbeschreibung erhält man</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Auch das zweite Symbol ist<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$.<ins class="diffchange diffchange-inline">&nbsp; </ins>Bei gleichem Vorgehen wie in der Aufgabenbeschreibung erhält man</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_2 \hspace{0.1cm}\underline{= 0}\hspace{0.05cm},\hspace{0.2cm}C_2 = 0.49 \cdot 0.7 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_2 \hspace{0.1cm}\underline{= 0}\hspace{0.05cm},\hspace{0.2cm}C_2 = 0.49 \cdot 0.7 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_2 \hspace{0.1cm} \underline{= 0.392}\hspace{0.05cm},\hspace{0.2cm}E_2 = C_1 \hspace{0.1cm}\underline{= 0.49} \hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_2 \hspace{0.1cm} \underline{= 0.392}\hspace{0.05cm},\hspace{0.2cm}E_2 = C_1 \hspace{0.1cm}\underline{= 0.49} \hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Für das dritte Symbol $\rm Y$ gelten nun die Begrenzungen $B_3 = C_2$ und $E_3 = D_2$:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Für das dritte Symbol<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Y$<ins class="diffchange diffchange-inline">&nbsp; </ins>gelten nun die Begrenzungen<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_3 = C_2$<ins class="diffchange diffchange-inline">&nbsp; </ins> und<ins class="diffchange diffchange-inline">&nbsp; </ins>$E_3 = D_2$:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_3 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}C_3 \hspace{0.1cm}\underline{= 0.3773}\hspace{0.05cm},\hspace{0.2cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_3 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}C_3 \hspace{0.1cm}\underline{= 0.3773}\hspace{0.05cm},\hspace{0.2cm}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_3 \hspace{0.1cm} \underline{= 0.3822}\hspace{0.05cm},\hspace{0.2cm}E_3 \hspace{0.1cm}\underline{= 0.392} \hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_3 \hspace{0.1cm} \underline{= 0.3822}\hspace{0.05cm},\hspace{0.2cm}E_3 \hspace{0.1cm}\underline{= 0.392} \hspace{0.05cm}.$$</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 1</u>:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 1</u>:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*</del>Aus $B_4 = 0.343 = B_3$ (abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein $\rm X$ war. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Aus<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_4 = 0.343 = B_3$<ins class="diffchange diffchange-inline">&nbsp; </ins>(abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$<ins class="diffchange diffchange-inline">&nbsp; </ins>war. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen. Man erkennt aus der Schraffierung, dass der zweite Lösungsvorschlag die richtige Symbolfolge angibt: &nbsp; $\rm XXYXXXZ$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen.<ins class="diffchange diffchange-inline">&nbsp; </ins>Man erkennt aus der Schraffierung, dass der zweite Lösungsvorschlag die richtige Symbolfolge angibt: &nbsp; $\rm XXYXXXZ$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite $\it \Delta$ kann wirklich gemäß dem Vorschlag 3 ermittelt werden. Es gilt:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite<ins class="diffchange diffchange-inline">&nbsp; </ins>$\it \Delta$<ins class="diffchange diffchange-inline">&nbsp; </ins>kann wirklich gemäß dem Vorschlag 3 ermittelt werden. Es gilt:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm},$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm},$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l129" >Zeile 129:</td>
<td colspan="2" class="diff-lineno">Zeile 133:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(6)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 2</u> &nbsp; &rArr; &nbsp; $r_2 = (0.010111)_{\text{binär}}$, wegen:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(6)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 2</u> &nbsp; &rArr; &nbsp; $r_2 = (0.010111)_{\text{binär}}$, wegen:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r_2 = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 1 \cdot 2^{-5} + 1 \cdot 2^{-6} = 0.359375\hspace{0.05cm}. $$ </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r_2 = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 1 \cdot 2^{-5} + 1 \cdot 2^{-6} = 0.359375\hspace{0.05cm}. $$ </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Der Vorschlag 1: &nbsp; $r_1 = (0.101100)_{\text{binär}}$ ist auszuschließen, da der zugehörige Dezimalwert $r_1 > 0.5$ ist. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Der Vorschlag 1: &nbsp; $r_1 = (0.101100)_{\text{binär}}$<ins class="diffchange diffchange-inline">&nbsp; </ins>ist auszuschließen, da der zugehörige Dezimalwert<ins class="diffchange diffchange-inline">&nbsp; </ins>$r_1 > 0.5$<ins class="diffchange diffchange-inline">&nbsp; </ins>ist. </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Auch der letzte Lösungsvorschlag ist falsch, da $r_3 = (0.001011)_{\text{binär}} < (0.01)_{\text{binär}} = (0.25)_{\text{dezimal}}$ <del class="diffchange diffchange-inline">ergibt</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Auch der letzte Lösungsvorschlag ist falsch, da<ins class="diffchange diffchange-inline">&nbsp; </ins>$r_3 = (0.001011)_{\text{binär}} < (0.01)_{\text{binär}} = (0.25)_{\text{dezimal}}$<ins class="diffchange diffchange-inline">&nbsp; sein wird</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=29399&oldid=prev
Guenter am 28. Januar 2020 um 13:05 Uhr
2020-01-28T13:05:11Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 28. Januar 2020, 13:05 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4" >Zeile 4:</td>
<td colspan="2" class="diff-lineno">Zeile 4:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2468__Inf_A_2_11.png|right|frame|Intervallschachtelung bei <br>arithmetischer Codierung]]</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2468__Inf_A_2_11.png|right|frame|Intervallschachtelung bei <br>arithmetischer Codierung]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die arithmetische Codierung ist eine spezielle Form der Entropiecodierung: &nbsp; Die Symbolwahrscheinlichkeiten müssen auch hier bekannt sein. In dieser Aufgabe gehen wir von $M = 3$ Symbolen aus, die wir mit $\rm X$, $\rm Y$ und $\rm Z$ benennen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die arithmetische Codierung ist eine spezielle Form der Entropiecodierung: &nbsp; Die Symbolwahrscheinlichkeiten müssen auch hier bekannt sein.<ins class="diffchange diffchange-inline">&nbsp; </ins>In dieser Aufgabe gehen wir von<ins class="diffchange diffchange-inline">&nbsp; </ins>$M = 3$<ins class="diffchange diffchange-inline">&nbsp; </ins>Symbolen aus, die wir mit<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Y$<ins class="diffchange diffchange-inline">&nbsp; </ins>und $\rm Z$<ins class="diffchange diffchange-inline">&nbsp; </ins>benennen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Während die Huffman&ndash;Codierung symbolweise erfolgt, wird bei der Arithmetischen Codierung (<del class="diffchange diffchange-inline">'''</del>AC<del class="diffchange diffchange-inline">'''</del>) eine Symbolfolge der Länge $N$ gemeinsam codiert. Das Codierergebnis ist ein reeller Zahlenwert $r$ aus dem Intervall</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Während die Huffman&ndash;Codierung symbolweise erfolgt, wird bei der Arithmetischen Codierung<ins class="diffchange diffchange-inline">&nbsp; $</ins>(<ins class="diffchange diffchange-inline">\rm </ins>AC)<ins class="diffchange diffchange-inline">$&nbsp; </ins>eine Symbolfolge der Länge<ins class="diffchange diffchange-inline">&nbsp; </ins>$N$<ins class="diffchange diffchange-inline">&nbsp; </ins>gemeinsam codiert.<ins class="diffchange diffchange-inline">&nbsp; </ins>Das Codierergebnis ist ein reeller Zahlenwert<ins class="diffchange diffchange-inline">&nbsp; </ins>$r$<ins class="diffchange diffchange-inline">&nbsp; </ins>aus dem Intervall</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$$I = \big[B, E \big) = \big[B, B +{\it \Delta} \big)\hspace{0.05cm}.$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$I = \big[B, <ins class="diffchange diffchange-inline">\ </ins>E \big) = \big[B, <ins class="diffchange diffchange-inline">\ </ins>B +{\it \Delta} \big)\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Diese Notation bedeutet:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Diese Notation bedeutet:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn $B$ gehört zum Intervall $I$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn<ins class="diffchange diffchange-inline">&nbsp; </ins>$B$<ins class="diffchange diffchange-inline">&nbsp; </ins>gehört zum Intervall<ins class="diffchange diffchange-inline">&nbsp; </ins>$I$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende $E$ ist nicht mehr in $I$ enthalten.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende<ins class="diffchange diffchange-inline">&nbsp; </ins>$E$<ins class="diffchange diffchange-inline">&nbsp; </ins>ist nicht mehr in<ins class="diffchange diffchange-inline">&nbsp; </ins>$I$<ins class="diffchange diffchange-inline">&nbsp; </ins>enthalten.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist ${\it} \Delta = E - B$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist<ins class="diffchange diffchange-inline">&nbsp; </ins>${\it} \Delta = E - B$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Von den unendlich vielen möglichen Werten $r \in I$ (da $r$ reellwertig ist, also kein Integer) wird derjenige Zahlenwert ausgewählt, der mit der geringsten Bitanzahl auskommt. Hierzu zwei Beispiele zur Verdeutlichung:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Von den unendlich vielen möglichen Werten<ins class="diffchange diffchange-inline">&nbsp; </ins>$r \in I<ins class="diffchange diffchange-inline">$&nbsp; </ins>$(<ins class="diffchange diffchange-inline">$</ins>da<ins class="diffchange diffchange-inline">&nbsp; </ins>$r$<ins class="diffchange diffchange-inline">&nbsp; </ins>reellwertig ist, also kein Integer<ins class="diffchange diffchange-inline">$</ins>)<ins class="diffchange diffchange-inline">$&nbsp; </ins>wird derjenige Zahlenwert ausgewählt, der mit der geringsten Bitanzahl auskommt.<ins class="diffchange diffchange-inline">&nbsp; </ins>Hierzu zwei Beispiele zur Verdeutlichung:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert &nbsp;$r = 3/4$ lässt sich mit zwei Bit darstellen:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert &nbsp;$r = 3/4$<ins class="diffchange diffchange-inline">&nbsp; </ins>lässt sich mit zwei Bit darstellen:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} = 0.75 \hspace{0.3cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} = 0.75 \hspace{0.3cm}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:}\hspace{0.<del class="diffchange diffchange-inline">15cm</del>} 0.11\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:}\hspace{0.<ins class="diffchange diffchange-inline">25cm</ins>} 0.11\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Code:} \hspace{0.<del class="diffchange diffchange-inline">15cm</del>} \boldsymbol{\rm 11} \hspace{0.05cm}, $$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Code:} \hspace{0.<ins class="diffchange diffchange-inline">25cm</ins>} \boldsymbol{\rm 11} \hspace{0.05cm}, $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert &nbsp;$r = 1/3$ benötigt dagegen unendlich viele Bit:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert &nbsp;$r = 1/3$<ins class="diffchange diffchange-inline">&nbsp; </ins>benötigt dagegen unendlich viele Bit:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:} \hspace{0.<del class="diffchange diffchange-inline">15cm</del>}0.011101\hspace{0.3cm}\Rightarrow\hspace{0.3cm}</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:} \hspace{0.<ins class="diffchange diffchange-inline">25cm</ins>}0.011101\hspace{0.3cm}\Rightarrow\hspace{0.3cm}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.<del class="diffchange diffchange-inline">15cm</del>} \boldsymbol{\rm 011101} \hspace{0.05cm}. $$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.<ins class="diffchange diffchange-inline">25cm</ins>} \boldsymbol{\rm 011101} \hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls &nbsp;$I$, gekennzeichnet durch den Beginn &nbsp;$B$&nbsp; sowie dem Ende &nbsp;$E$&nbsp; bzw. der Breite &nbsp;$\Delta$. </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls &nbsp;$I$, gekennzeichnet durch den Beginn &nbsp;$B$&nbsp; sowie dem Ende &nbsp;$E$&nbsp; bzw. der Breite &nbsp;$\Delta$. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Diese Bestimmung geschieht entsprechend der Intervallschachtelung in obiger Grafik. </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Diese Bestimmung geschieht entsprechend der Intervallschachtelung in obiger Grafik. </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen $\rm XXY$ beginnt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm XXY$<ins class="diffchange diffchange-inline">&nbsp; </ins>beginnt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Algorithmus funktioniert wie folgt:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Algorithmus funktioniert wie folgt:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Vor Beginn (quasi beim nullten Symbol) wird der gesamte Wahrscheinlichkeitsbereich nach den Wahrscheinlichkeiten $p_{\rm X}$, $p_{\rm Y}$ und $p_{\rm Z}$ in drei Bereiche unterteilt. Die Grenzen liegen bei</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Vor Beginn<ins class="diffchange diffchange-inline">&nbsp; </ins>(quasi beim nullten Symbol)<ins class="diffchange diffchange-inline">&nbsp; </ins>wird der gesamte Wahrscheinlichkeitsbereich nach den Wahrscheinlichkeiten<ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm X}$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm Y}$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$p_{\rm Z}$<ins class="diffchange diffchange-inline">&nbsp; </ins>in drei Bereiche unterteilt.<ins class="diffchange diffchange-inline">&nbsp; </ins>Die Grenzen liegen bei</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.<del class="diffchange diffchange-inline">2cm</del>}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.<del class="diffchange diffchange-inline">2cm</del>}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.<del class="diffchange diffchange-inline">2cm</del>} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.<ins class="diffchange diffchange-inline">4cm</ins>}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.<ins class="diffchange diffchange-inline">4cm</ins>}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.<ins class="diffchange diffchange-inline">4cm</ins>} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist $\rm X$ <del class="diffchange diffchange-inline">&nbsp; &#8658; </del>&nbsp; das ausgewählte Intervall wird durch $B_0$ und $C_0$ begrenzt. Dieses Intervall wird mit neuem Beginn $B_1 = B_0$ und neuem Ende $E_1 = C_0$ in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt. Die Zwischenwerte sind $C_1$ und $D_1$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$<ins class="diffchange diffchange-inline">. Das bedeutet: </ins>&nbsp; das ausgewählte Intervall wird durch<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_0$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$C_0$<ins class="diffchange diffchange-inline">&nbsp; </ins>begrenzt.<ins class="diffchange diffchange-inline">&nbsp; </ins>Dieses Intervall wird mit neuem Beginn<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_1 = B_0$<ins class="diffchange diffchange-inline">&nbsp; </ins>und neuem Ende<ins class="diffchange diffchange-inline">&nbsp; </ins>$E_1 = C_0$<ins class="diffchange diffchange-inline">&nbsp; </ins>in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt.<ins class="diffchange diffchange-inline">&nbsp; </ins>Die Zwischenwerte sind<ins class="diffchange diffchange-inline">&nbsp; </ins>$C_1$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$D_1$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe. Beispielsweise sollen in der Teilaufgabe '''(2)''' die Grenzen $B_2$, $C_2$, $D_2$ und $E_2$ für das zweite Symbol $\rm X$ ermittelt werden und in der Teilaufgabe '''(3)''' die Grenzen $B_3$, $C_3$, $D_3$ und $E_3$ für das dritte Symbol $\rm Y$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe.<ins class="diffchange diffchange-inline">&nbsp; </ins>Beispielsweise sollen in der Teilaufgabe<ins class="diffchange diffchange-inline">&nbsp; </ins>'''(2)'''<ins class="diffchange diffchange-inline">&nbsp; </ins>die Grenzen<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_2$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$C_2$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$D_2$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$E_2$<ins class="diffchange diffchange-inline">&nbsp; </ins>für das zweite Symbol<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$<ins class="diffchange diffchange-inline">&nbsp; </ins> ermittelt werden und in der Teilaufgabe<ins class="diffchange diffchange-inline">&nbsp; </ins>'''(3)'''<ins class="diffchange diffchange-inline">&nbsp; </ins>die Grenzen<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_3$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$C_3$,<ins class="diffchange diffchange-inline">&nbsp; </ins>$D_3$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$E_3$<ins class="diffchange diffchange-inline">&nbsp; </ins>für das dritte Symbol<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Y$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l41" >Zeile 41:</td>
<td colspan="2" class="diff-lineno">Zeile 41:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''Hinweise:'' </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:Aufgabe_2.11:_Nochmals_Arithmetische_Codierung|Aufgabe 2.11Z]] behandelt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der<ins class="diffchange diffchange-inline">&nbsp; </ins>[[Aufgaben:Aufgabe_2.11:_Nochmals_Arithmetische_Codierung|Aufgabe 2.11Z]]<ins class="diffchange diffchange-inline">&nbsp; </ins>behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l51" >Zeile 51:</td>
<td colspan="2" class="diff-lineno">Zeile 51:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><quiz display=simple></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Welche Wahrscheinlichkeiten <del class="diffchange diffchange-inline">sind </del>der Grafik <del class="diffchange diffchange-inline">zugrundegelegt</del>?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Welche Wahrscheinlichkeiten <ins class="diffchange diffchange-inline">liegen </ins>der Grafik <ins class="diffchange diffchange-inline">zugrunde</ins>?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm X} \hspace{0.10cm} = \ $ { 0.7 3% }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm X} \hspace{0.10cm} = \ $ { 0.7 3% }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l58" >Zeile 58:</td>
<td colspan="2" class="diff-lineno">Zeile 58:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des zweiten Symbols $\rm X$?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des zweiten Symbols<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_2 \hspace{0.12cm} = \ $ { 0. }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_2 \hspace{0.12cm} = \ $ { 0. }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l66" >Zeile 66:</td>
<td colspan="2" class="diff-lineno">Zeile 66:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des dritten Symbols $\rm Y$?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des dritten Symbols<ins class="diffchange diffchange-inline">&nbsp; </ins> $\rm Y$?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_3 \hspace{0.12cm} = \ $ { 0.343 1% }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_3 \hspace{0.12cm} = \ $ { 0.343 1% }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l74" >Zeile 74:</td>
<td colspan="2" class="diff-lineno">Zeile 74:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Nach der Codierung des vierten Symbols ist $B_4 = 0.343$. Was folgt daraus?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Nach der Codierung des vierten Symbols ist<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_4 = 0.343$.<ins class="diffchange diffchange-inline">&nbsp; </ins>Was folgt daraus?</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>|type="<del class="diffchange diffchange-inline">[]</del>"}</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>|type="<ins class="diffchange diffchange-inline">()</ins>"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ Das vierte Symbol war $\rm X$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ Das vierte Symbol war<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm X$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war $\rm Y$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Y$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war $\rm Z$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm Z$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Nach weiteren Symbolen wird das Intervall durch $B_7 = 0.3564456$ und $E_7 = 0.359807$ begrenzt. Welche Aussagen treffen zu?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Nach weiteren Symbolen wird das Intervall durch<ins class="diffchange diffchange-inline">&nbsp; </ins>$B_7 = 0.3564456$<ins class="diffchange diffchange-inline">&nbsp; </ins>und<ins class="diffchange diffchange-inline">&nbsp; </ins>$E_7 = 0.359807$<ins class="diffchange diffchange-inline">&nbsp; </ins>begrenzt.<ins class="diffchange diffchange-inline">&nbsp; </ins>Welche Aussagen treffen zu?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Die zur Codierung anstehende Symbolfolge lautet $\rm XXYXXZX$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Die zur Codierung anstehende Symbolfolge lautet<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm XXYXXZX$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ Die zur Codierung anstehende Symbolfolge lautet $\rm XXYXXXZ$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ Die zur Codierung anstehende Symbolfolge lautet<ins class="diffchange diffchange-inline">&nbsp; </ins>$\rm XXYXXXZ$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ Die Breite des resultierenden Intervalls ist ${\it \Delta} = p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z}$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ Die Breite des resultierenden Intervalls ist<ins class="diffchange diffchange-inline">&nbsp; </ins>${\it \Delta} = p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z}$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=26380&oldid=prev
Guenter am 2. Oktober 2018 um 12:03 Uhr
2018-10-02T12:03:40Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 2. Oktober 2018, 12:03 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l100" >Zeile 100:</td>
<td colspan="2" class="diff-lineno">Zeile 100:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Musterlösung===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Musterlösung===</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Kopf}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{ML-Kopf}}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2469__Inf_A_2_11_ML.png|right|Intervallschachtelung mit allen Zahlenwerten]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2469__Inf_A_2_11_ML.png|right<ins class="diffchange diffchange-inline">|frame</ins>|Intervallschachtelung mit allen Zahlenwerten]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Aus der Grafik auf der Angabenseite kann man die Wahrscheinlichkeiten ablesen:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(1)'''&nbsp; Aus der Grafik auf der Angabenseite kann man die Wahrscheinlichkeiten ablesen:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm X} = 0.7\hspace{0.05cm},\hspace{0.2cm}p_{\rm Y} = 0.1\hspace{0.05cm},\hspace{0.2cm}p_{\rm Z} = 0.2\hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$p_{\rm X} = 0.7\hspace{0.05cm},\hspace{0.2cm}p_{\rm Y} = 0.1\hspace{0.05cm},\hspace{0.2cm}p_{\rm Z} = 0.2\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Auch das zweite Symbol ist <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b></del>. Bei gleichem Vorgehen wie in der Aufgabenbeschreibung erhält man</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(2)'''&nbsp; Auch das zweite Symbol ist <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>. Bei gleichem Vorgehen wie in der Aufgabenbeschreibung erhält man</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_2 \hspace{0.1cm}\underline{= 0}\hspace{0.05cm},\hspace{0.2cm}C_2 = 0.49 \cdot 0.7 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_2 \hspace{0.1cm}\underline{= 0}\hspace{0.05cm},\hspace{0.2cm}C_2 = 0.49 \cdot 0.7 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_2 \hspace{0.1cm} \underline{= 0.392}\hspace{0.05cm},\hspace{0.2cm}E_2 = C_1 \hspace{0.1cm}\underline{= 0.49} \hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_2 \hspace{0.1cm} \underline{= 0.392}\hspace{0.05cm},\hspace{0.2cm}E_2 = C_1 \hspace{0.1cm}\underline{= 0.49} \hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Für das dritte Symbol <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b> </del>gelten nun die Begrenzungen $B_3 = C_2$ und $E_3 = D_2$:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(3)'''&nbsp; Für das dritte Symbol <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$ </ins>gelten nun die Begrenzungen $B_3 = C_2$ und $E_3 = D_2$:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_3 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}C_3 \hspace{0.1cm}\underline{= 0.3773}\hspace{0.05cm},\hspace{0.2cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_3 \hspace{0.1cm}\underline{= 0.343}\hspace{0.05cm},\hspace{0.2cm}C_3 \hspace{0.1cm}\underline{= 0.3773}\hspace{0.05cm},\hspace{0.2cm}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_3 \hspace{0.1cm} \underline{= 0.3822}\hspace{0.05cm},\hspace{0.2cm}E_3 \hspace{0.1cm}\underline{= 0.392} \hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>D_3 \hspace{0.1cm} \underline{= 0.3822}\hspace{0.05cm},\hspace{0.2cm}E_3 \hspace{0.1cm}\underline{= 0.392} \hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; Aus $B_4 = 0.343 = B_3$ (abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b> </del>war <del class="diffchange diffchange-inline">&nbsp; &#8658; &nbsp; <u>Lösungsvorschlag 1</del>.<del class="diffchange diffchange-inline"></u></del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''(4)'''&nbsp; <ins class="diffchange diffchange-inline">Richtig ist der <u>Lösungsvorschlag 1</u>:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Aus $B_4 = 0.343 = B_3$ (abzulesen in der Grafik auf dem Angabenblatt) folgt zwingend, dass das vierte Quellensymbol ein <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$ </ins>war. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(5)'''&nbsp; Richtig sind die <u>Lösungsvorschläge 2 und 3:</u></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen. Man erkennt aus der Schraffierung, dass der zweite Lösungsvorschlag die richtige Symbolfolge angibt: <del class="diffchange diffchange-inline"><b></del>XXYXXXZ<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Grafik zeigt die Intervallschachtelung mit allen bisherigen Ergebnissen. Man erkennt aus der Schraffierung, dass der zweite Lösungsvorschlag die richtige Symbolfolge angibt: <ins class="diffchange diffchange-inline">&nbsp; $\rm </ins>XXYXXXZ<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite $\it \Delta$ kann wirklich gemäß dem Vorschlag 3 ermittelt werden:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite $\it \Delta$ kann wirklich gemäß dem Vorschlag 3 ermittelt werden<ins class="diffchange diffchange-inline">. Es gilt</ins>:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm}$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} = 0.359807 - 0.3564456 = 0.003614 \hspace{0.05cm}<ins class="diffchange diffchange-inline">,</ins>$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$${\it \Delta} =p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z} = 0.7^5 \cdot 0.1 \cdot 0.2 = 0.003614 </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\hspace{0.05cm}. $$</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(6)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 2</u> &nbsp; &rArr; &nbsp; $r_2 = (0.010111)_{\text{binär}}$, wegen:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''(6)'''&nbsp; Richtig ist der <u>Lösungsvorschlag 2</u> &nbsp; &rArr; &nbsp; $r_2 = (0.010111)_{\text{binär}}$, wegen:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r_2 = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 1 \cdot 2^{-5} + 1 \cdot 2^{-6} = 0.359375\hspace{0.05cm}. $$ </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r_2 = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 0 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 1 \cdot 2^{-5} + 1 \cdot 2^{-6} = 0.359375\hspace{0.05cm}. $$ </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Der Vorschlag 1: $r_1 = (0.101100)_{\text{binär}}$ ist auszuschließen, da der zugehörige Dezimalwert $r_1 > 0.5$ ist. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Der Vorschlag 1: <ins class="diffchange diffchange-inline">&nbsp; </ins>$r_1 = (0.101100)_{\text{binär}}$ ist auszuschließen, da der zugehörige Dezimalwert $r_1 > 0.5$ ist. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Auch der letzte Lösungsvorschlag ist falsch, da $r_3 = (0.001011)_{\text{binär}} < (0.01)_{\text{binär}} = (0.25)_{\text{dezimal}}$ ergibt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Auch der letzte Lösungsvorschlag ist falsch, da $r_3 = (0.001011)_{\text{binär}} < (0.01)_{\text{binär}} = (0.25)_{\text{dezimal}}$ ergibt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=26379&oldid=prev
Guenter am 2. Oktober 2018 um 11:53 Uhr
2018-10-02T11:53:32Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 2. Oktober 2018, 11:53 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Zeile 43:</td>
<td colspan="2" class="diff-lineno">Zeile 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:Aufgabe_2.11:_Nochmals_Arithmetische_Codierung|<del class="diffchange diffchange-inline">Zusatzaufgabe </del>2.11Z]] behandelt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:Aufgabe_2.11:_Nochmals_Arithmetische_Codierung|<ins class="diffchange diffchange-inline">Aufgabe </ins>2.11Z]] behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Fragebogen===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Fragebogen===</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l51" >Zeile 51:</td>
<td colspan="2" class="diff-lineno">Zeile 53:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Welche Wahrscheinlichkeiten sind der Grafik zugrundegelegt?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Welche Wahrscheinlichkeiten sind der Grafik zugrundegelegt?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm X} \hspace{0.10cm} = $ { 0.7 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm X} \hspace{0.10cm} = <ins class="diffchange diffchange-inline">\ </ins>$ { 0.7 3% }</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm Y} \hspace{0.10cm} = $ { 0.1 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm Y} \hspace{0.10cm} = <ins class="diffchange diffchange-inline"> \ </ins>$ { 0.1 3% }</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm Z} \hspace{0.15cm} = $ { 0.2 3% }</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$p_{\rm Z} \hspace{0.15cm} = <ins class="diffchange diffchange-inline"> \ </ins>$ { 0.2 3% }</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des zweiten Symbols <del class="diffchange diffchange-inline">&bdquo;'''</del>X<del class="diffchange diffchange-inline">'''&rdquo;</del>?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des zweiten Symbols <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_2 \hspace{0.12cm} = \ $ { 0. }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_2 \hspace{0.12cm} = \ $ { 0. }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l64" >Zeile 64:</td>
<td colspan="2" class="diff-lineno">Zeile 66:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des dritten Symbols <del class="diffchange diffchange-inline">&bdquo;'''</del>Y<del class="diffchange diffchange-inline">'''&rdquo;</del>?</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{Wie lauten die Bereichsgrenzen nach der Codierung des dritten Symbols <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$</ins>?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="{}"}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_3 \hspace{0.12cm} = \ $ { 0.343 1% }</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$B_3 \hspace{0.12cm} = \ $ { 0.343 1% }</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l74" >Zeile 74:</td>
<td colspan="2" class="diff-lineno">Zeile 76:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Nach der Codierung des vierten Symbols ist $B_4 = 0.343$. Was folgt daraus?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Nach der Codierung des vierten Symbols ist $B_4 = 0.343$. Was folgt daraus?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ Das vierte Symbol war <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ Das vierte Symbol war <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war <del class="diffchange diffchange-inline"><b></del>Z<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Das vierte Symbol war <ins class="diffchange diffchange-inline">$\rm </ins>Z<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Nach weiteren Symbolen wird das Intervall durch $B_7 = 0.3564456$ und $E_7 = 0.359807$ begrenzt. Welche Aussagen treffen zu?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Nach weiteren Symbolen wird das Intervall durch $B_7 = 0.3564456$ und $E_7 = 0.359807$ begrenzt. Welche Aussagen treffen zu?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|type="[]"}</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>- Die zur Codierung anstehende Symbolfolge lautet <del class="diffchange diffchange-inline"><b></del>XXYXXZX<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>- Die zur Codierung anstehende Symbolfolge lautet <ins class="diffchange diffchange-inline">$\rm </ins>XXYXXZX<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>+ Die zur Codierung anstehende Symbolfolge lautet <del class="diffchange diffchange-inline"><b></del>XXYXXXZ<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>+ Die zur Codierung anstehende Symbolfolge lautet <ins class="diffchange diffchange-inline">$\rm </ins>XXYXXXZ<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ Die Breite des resultierenden Intervalls ist ${\it \Delta} = p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z}$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>+ Die Breite des resultierenden Intervalls ist ${\it \Delta} = p_{\rm X}^5 \cdot p_{\rm Y} \cdot p_{\rm Z}$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=26378&oldid=prev
Guenter am 2. Oktober 2018 um 11:46 Uhr
2018-10-02T11:46:31Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 2. Oktober 2018, 11:46 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l43" >Zeile 43:</td>
<td colspan="2" class="diff-lineno">Zeile 43:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Aufgabe gehört zum Kapitel [[Informationstheorie/Weitere_Quellencodierverfahren|Weitere Quellencodierverfahren]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:<del class="diffchange diffchange-inline">2</del>.<del class="diffchange diffchange-inline">12_Nochmals_Arithmetische_Codierung</del>|Zusatzaufgabe 2.11Z]] behandelt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:<ins class="diffchange diffchange-inline">Aufgabe_2</ins>.<ins class="diffchange diffchange-inline">11:_Nochmals_Arithmetische_Codierung</ins>|Zusatzaufgabe 2.11Z]] behandelt.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
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Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=26377&oldid=prev
Guenter am 2. Oktober 2018 um 11:45 Uhr
2018-10-02T11:45:19Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 2. Oktober 2018, 11:45 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Zeile 3:</td>
<td colspan="2" class="diff-lineno">Zeile 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2468__Inf_A_2_11.png|right|Intervallschachtelung bei arithmetischer Codierung]]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>[[Datei:P_ID2468__Inf_A_2_11.png|right<ins class="diffchange diffchange-inline">|frame</ins>|Intervallschachtelung bei <ins class="diffchange diffchange-inline"><br></ins>arithmetischer Codierung]]</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Die arithmetische Codierung ist eine spezielle Form der Entropiecodierung: <del class="diffchange diffchange-inline">Auch </del>hier <del class="diffchange diffchange-inline">müssen die Symbolwahrscheinlichkeiten </del>bekannt sein. In dieser Aufgabe gehen wir von $M = 3$ Symbolen aus, die wir mit <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b></del>, <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b>, <b></del>Z<del class="diffchange diffchange-inline"></b> </del>benennen.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Die arithmetische Codierung ist eine spezielle Form der Entropiecodierung: <ins class="diffchange diffchange-inline">&nbsp; Die Symbolwahrscheinlichkeiten müssen auch </ins>hier bekannt sein. In dieser Aufgabe gehen wir von $M = 3$ Symbolen aus, die wir mit <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$</ins>, <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$ und $\rm </ins>Z<ins class="diffchange diffchange-inline">$ </ins>benennen.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Während die Huffman&ndash;Codierung symbolweise erfolgt, wird bei der Arithmetischen Codierung (AC) eine Symbolfolge der Länge $N$ gemeinsam codiert. Das Codierergebnis ist ein reeller Zahlenwert $r$ aus dem Intervall</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Während die Huffman&ndash;Codierung symbolweise erfolgt, wird bei der Arithmetischen Codierung (<ins class="diffchange diffchange-inline">'''</ins>AC<ins class="diffchange diffchange-inline">'''</ins>) eine Symbolfolge der Länge $N$ gemeinsam codiert. Das Codierergebnis ist ein reeller Zahlenwert $r$ aus dem Intervall</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:$$I = [B, E) = [B, B +{\it \Delta} )\hspace{0.05cm}.$$</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:$$I = <ins class="diffchange diffchange-inline">\big</ins>[B, E <ins class="diffchange diffchange-inline">\big</ins>) = <ins class="diffchange diffchange-inline">\big</ins>[B, B +{\it \Delta} <ins class="diffchange diffchange-inline">\big</ins>)\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Diese Notation bedeutet:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Diese Notation bedeutet:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn $B$ gehört zum Intervall $I$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Der Beginn $B$ gehört zum Intervall $I$.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende $E$ ist nicht mehr in $I$ enthalten.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Das Ende $E$ ist nicht mehr in $I$ enthalten.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist ${\it} \Delta = E - B$.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Die Intervallbreite ist ${\it} \Delta = E - B$.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Von den unendlich vielen möglichen Werten $r \in I$ (da $r$ reellwertig ist, also kein Integer) wird derjenige Zahlenwert ausgewählt, der mit der geringsten Bitanzahl auskommt. Hierzu zwei Beispiele zur Verdeutlichung:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Von den unendlich vielen möglichen Werten $r \in I$ (da $r$ reellwertig ist, also kein Integer) wird derjenige Zahlenwert ausgewählt, der mit der geringsten Bitanzahl auskommt. Hierzu zwei Beispiele zur Verdeutlichung:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert $r = 3/4$ lässt sich mit zwei Bit darstellen:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert <ins class="diffchange diffchange-inline">&nbsp;</ins>$r = 3/4$ lässt sich mit zwei Bit darstellen:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} = 0.75 \hspace{0.3cm}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 1 \cdot 2^{-1} + 1 \cdot 2^{-2} = 0.75 \hspace{0.3cm}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:}\hspace{0.15cm} 0.11\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\Rightarrow\hspace{0.3cm}\text{binär:}\hspace{0.15cm} 0.11\hspace{0.3cm}\Rightarrow\hspace{0.3cm}\text</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Code:} \hspace{0.15cm} \boldsymbol{\rm 11} \hspace{0.05cm}, $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{Code:} \hspace{0.15cm} \boldsymbol{\rm 11} \hspace{0.05cm}, $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert $r = 1/3$ benötigt dagegen unendlich viele Bit:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Der Dezimalwert <ins class="diffchange diffchange-inline">&nbsp;</ins>$r = 1/3$ benötigt dagegen unendlich viele Bit:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$r = 0 \cdot 2^{-1} + 1 \cdot 2^{-2} + 1 \cdot 2^{-3}+ 1 \cdot 2^{-4}+ 0 \cdot 2^{-5} + 1 \cdot 2^{-6} + \hspace{0.05cm}\text{...}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >Zeile 25:</td>
<td colspan="2" class="diff-lineno">Zeile 26:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.15cm} \boldsymbol{\rm 011101} \hspace{0.05cm}. $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\text{Code:} \hspace{0.15cm} \boldsymbol{\rm 011101} \hspace{0.05cm}. $$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls $I$, gekennzeichnet durch den Beginn $B$ sowie dem Ende $E$ bzw. der Breite $\Delta$. Diese Bestimmung geschieht entsprechend der Intervallschachtelung in obiger Grafik. An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen <del class="diffchange diffchange-inline"><b></del>XXY<del class="diffchange diffchange-inline"></b> </del>beginnt.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In dieser Aufgabe beschränken wir uns auf die Bestimmung des aktuellen Intervalls <ins class="diffchange diffchange-inline">&nbsp;</ins>$I$, gekennzeichnet durch den Beginn <ins class="diffchange diffchange-inline">&nbsp;</ins>$B$<ins class="diffchange diffchange-inline">&nbsp; </ins>sowie dem Ende <ins class="diffchange diffchange-inline">&nbsp;</ins>$E$<ins class="diffchange diffchange-inline">&nbsp; </ins>bzw. der Breite <ins class="diffchange diffchange-inline">&nbsp;</ins>$\Delta$. </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>Diese Bestimmung geschieht entsprechend der Intervallschachtelung in obiger Grafik. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*</ins>An der Schraffierung ist zu erkennen, dass die Folge mit den Ternärsymbolen <ins class="diffchange diffchange-inline">$\rm </ins>XXY<ins class="diffchange diffchange-inline">$ </ins>beginnt.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><br clear=all></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Algorithmus funktioniert wie folgt:</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Der Algorithmus funktioniert wie folgt:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Vor Beginn (quasi beim nullten Symbol) wird der gesamte Wahrscheinlichkeitsbereich nach den Wahrscheinlichkeiten $p_{\rm X}$, $p_{\rm Y}$ und $p_{\rm Z}$ in drei Bereiche unterteilt. Die Grenzen liegen bei</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Vor Beginn (quasi beim nullten Symbol) wird der gesamte Wahrscheinlichkeitsbereich nach den Wahrscheinlichkeiten $p_{\rm X}$, $p_{\rm Y}$ und $p_{\rm Z}$ in drei Bereiche unterteilt. Die Grenzen liegen bei</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.2cm}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.2cm}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.2cm} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:$$B_0 = 0\hspace{0.05cm},\hspace{0.2cm}C_0 = p_{\rm X}\hspace{0.05cm},\hspace{0.2cm}D_0 = p_{\rm X} + p_{\rm Y}\hspace{0.05cm},\hspace{0.2cm} E_0 = p_{\rm X} + p_{\rm Y}+ p_{\rm Z} = 1\hspace{0.05cm}.$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b> </del>&nbsp;&#8658;&nbsp; das ausgewählte Intervall wird durch $B_0$ und $C_0$ begrenzt. Dieses Intervall wird mit neuem Beginn $B_1 = B_0$ und neuem Ende $E_1 = C_0$ in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt. Die Zwischenwerte sind $C_1$ und $D_1$.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Das erste Symbol der zu codierenden Folge ist <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$ </ins>&nbsp; &#8658; &nbsp; das ausgewählte Intervall wird durch $B_0$ und $C_0$ begrenzt. Dieses Intervall wird mit neuem Beginn $B_1 = B_0$ und neuem Ende $E_1 = C_0$ in gleicher Weise aufgeteilt wie der Gesamtbereich im nullten Schritt. Die Zwischenwerte sind $C_1$ und $D_1$.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe. Beispielsweise sollen in der Teilaufgabe (2) die Grenzen $B_2$, $C_2$, $D_2$ und $E_2$ für das zweite Symbol <del class="diffchange diffchange-inline"><b></del>X<del class="diffchange diffchange-inline"></b> </del> ermittelt werden und in der Teilaufgabe (3) <del class="diffchange diffchange-inline">entsprechend </del>die Grenzen $B_3$, $C_3$, $D_3$ und $E_3$ für das dritte Symbol <del class="diffchange diffchange-inline"><b></del>Y<del class="diffchange diffchange-inline"></b></del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Die weitere Intervall&ndash;Aufteilung ist Ihre Aufgabe. Beispielsweise sollen in der Teilaufgabe <ins class="diffchange diffchange-inline">'''</ins>(2)<ins class="diffchange diffchange-inline">''' </ins>die Grenzen $B_2$, $C_2$, $D_2$ und $E_2$ für das zweite Symbol <ins class="diffchange diffchange-inline">$\rm </ins>X<ins class="diffchange diffchange-inline">$ </ins> ermittelt werden und in der Teilaufgabe <ins class="diffchange diffchange-inline">'''</ins>(3)<ins class="diffchange diffchange-inline">''' </ins>die Grenzen $B_3$, $C_3$, $D_3$ und $E_3$ für das dritte Symbol <ins class="diffchange diffchange-inline">$\rm </ins>Y<ins class="diffchange diffchange-inline">$</ins>.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
Guenter
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=24802&oldid=prev
Mwiki-lnt: Textersetzung - „*Sollte die Eingabe des Zahlenwertes „0” erforderlich sein, so geben Sie bitte „0.” ein.“ durch „ “
2018-05-29T12:02:41Z
<p>Textersetzung - „*Sollte die Eingabe des Zahlenwertes „0” erforderlich sein, so geben Sie bitte „0.” ein.“ durch „ “</p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="de">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Version vom 29. Mai 2018, 12:02 Uhr</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39" >Zeile 39:</td>
<td colspan="2" class="diff-lineno">Zeile 39:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Insbesondere wird Bezug genommen auf die Seite [[Informationstheorie/Weitere_Quellencodierverfahren#Arithmetische_Codierung|Arithmetische Codierung]].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:2.12_Nochmals_Arithmetische_Codierung|Zusatzaufgabe 2.11Z]] behandelt.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Die Binärdarstellung des ausgewählten Intervalls wird in der [[Aufgaben:2.12_Nochmals_Arithmetische_Codierung|Zusatzaufgabe 2.11Z]] behandelt.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*Sollte die Eingabe des Zahlenwertes &bdquo;0&rdquo; erforderlich sein, so geben Sie bitte &bdquo;0.&rdquo; ein.</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"> </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Fragebogen===</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>===Fragebogen===</div></td></tr>
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Mwiki-lnt
https://www.lntwww.de/index.php?title=Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung&diff=21839&oldid=prev
Guenter: Guenter verschob die Seite Aufgaben:2.11 Arithmetische Codierung nach Aufgaben:Aufgabe 2.11: Arithmetische Codierung
2018-01-03T14:01:11Z
<p>Guenter verschob die Seite <a href="/Aufgaben:2.11_Arithmetische_Codierung" class="mw-redirect" title="Aufgaben:2.11 Arithmetische Codierung">2.11 Arithmetische Codierung</a> nach <a href="/Aufgaben:Aufgabe_2.11:_Arithmetische_Codierung" title="Aufgaben:Aufgabe 2.11: Arithmetische Codierung">Aufgabe 2.11: Arithmetische Codierung</a></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<tr class="diff-title" lang="de">
<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">← Nächstältere Version</td>
<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">Version vom 3. Januar 2018, 14:01 Uhr</td>
</tr><tr><td colspan="2" class="diff-notice" lang="de"><div class="mw-diff-empty">(kein Unterschied)</div>
</td></tr></table>
Guenter