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Pfeile für die Leserichtung korrigiert
Es wurden die Pfeile bei der Umrechnung der ganzen Dezimalzahlen in Binärzahlen umgedreht, da dort von unten nach oben gelesen werden muss, und Pfeile bei den gebrochenen Zahlen hinzugefügt.
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09_Rechnerarithmetik.md

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@@ -203,11 +203,11 @@ style="width: 80%; min-width: 420px; max-width: 720px;"
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Der Teiler definiert das avisierte Zahlensystem
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|
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v
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29 / 2 = 14 Rest 1 |
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29 / 2 = 14 Rest 1 ^
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14 / 2 = 7 Rest 0 |
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7 / 2 = 3 Rest 1 |
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3 / 2 = 1 Rest 1 |
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1 / 2 = 0 Rest 1 v .
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1 / 2 = 0 Rest 1 | .
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```
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@@ -235,7 +235,7 @@ __Beispiel:__ $242_{10}$ in binär
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style="width: 80%; min-width: 420px; max-width: 720px;"
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-->
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```ascii
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523 / 2 = 261 Rest 1 |
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523 / 2 = 261 Rest 1 ^
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261 / 2 = 130 Rest 1 |
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130 / 2 = 65 Rest 0 |
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65 / 2 = 32 Rest 1 |
@@ -244,7 +244,7 @@ style="width: 80%; min-width: 420px; max-width: 720px;"
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8 / 2 = 4 Rest 0 |
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4 / 2 = 2 Rest 0 |
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2 / 2 = 1 Rest 0 |
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1 / 2 = 0 Rest 1 v
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1 / 2 = 0 Rest 1 |
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```
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$523_{10}$=$1000001011_{2}$
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@@ -290,11 +290,11 @@ style="width: 80%; min-width: 420px; max-width: 720px;"
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Der Faktor definiert das avisierte Zahlensystem
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v
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0.28125 ∙ 2 = 0.5625 "<" 1 -> 0 Rest 0.5625
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0.5625 ∙ 2 = 1.125 ">" 1 -> 1 Rest 0.125
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0.125 ∙ 2 = 0.25 "<" 1 -> 0 Rest 0.25
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0.25 ∙ 2 = 0.5 "<" 1 -> 0 Rest 0.5
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0.5 ∙ 2 = 1 "<="1 -> 1 Rest 0 .
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0.28125 ∙ 2 = 0.5625 "<" 1 -> 0 | Rest 0.5625
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0.5625 ∙ 2 = 1.125 ">" 1 -> 1 | Rest 0.125
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0.125 ∙ 2 = 0.25 "<" 1 -> 0 | Rest 0.25
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0.25 ∙ 2 = 0.5 "<" 1 -> 0 | Rest 0.5
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0.5 ∙ 2 = 1 "<="1 -> 1 v Rest 0 .
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```
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@@ -308,15 +308,15 @@ Ergebnis $0.28125_{10} = 0.25 + 0.03125 = 0.01001$
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style="width: 80%; min-width: 420px; max-width: 720px;"
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-->
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```ascii
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0.1 ∙ 2 = 0.2 0 Rest 0.2
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0.2 ∙ 2 = 0.4 0 Rest 0.4
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0.4 ∙ 2 = 0.8 0 Rest 0.8
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0.8 ∙ 2 = 1.6 1 Rest 0.6
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0.6 ∙ 2 = 1.2 1 Rest 0.2
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0.2 ∙ 2 = 0.4 0 Rest 0.4
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0.4 ∙ 2 = 0.8 0 Rest 0.8
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0.8 ∙ 2 = 1.6 1 Rest 0.6
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0.6 ∙ 2 = 1.2 1 Rest 0.2 .
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0.1 ∙ 2 = 0.2 0 | Rest 0.2
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0.2 ∙ 2 = 0.4 0 | Rest 0.4
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0.4 ∙ 2 = 0.8 0 | Rest 0.8
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0.8 ∙ 2 = 1.6 1 | Rest 0.6
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0.6 ∙ 2 = 1.2 1 | Rest 0.2
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0.2 ∙ 2 = 0.4 0 | Rest 0.4
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0.4 ∙ 2 = 0.8 0 | Rest 0.8
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0.8 ∙ 2 = 1.6 1 | Rest 0.6
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0.6 ∙ 2 = 1.2 1 v Rest 0.2 .
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```
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Ergebnis Offenbar ist für den Wert $0.1_{10}$ keine exakte Repräsentation im dualen System möglich $0,0001100110011...._2$. Welche Konsequenzen hat das?
@@ -391,14 +391,14 @@ Kein Überlauf!
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style="width: 80%; min-width: 420px; max-width: 720px;"
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-->
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```ascii
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55 / 2 = 27 Rest 1 | 214 / 2 = 107 Rest 0 |
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55 / 2 = 27 Rest 1 ^ 214 / 2 = 107 Rest 0 ^
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27 / 2 = 13 Rest 1 | 107 / 2 = 53 Rest 1 |
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13 / 2 = 6 Rest 1 | 53 / 2 = 26 Rest 1 |
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6 / 2 = 3 Rest 0 | 26 / 2 = 13 Rest 0 |
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3 / 2 = 1 Rest 1 | 13 / 2 = 6 Rest 1 |
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1 / 2 = 0 Rest 1 v 6 / 2 = 3 Rest 0 |
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1 / 2 = 0 Rest 1 | 6 / 2 = 3 Rest 0 |
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3 / 2 = 1 Rest 1 |
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1 / 2 = 0 Rest 1 v .
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1 / 2 = 0 Rest 1 | .
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```
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