From 21c8023e7013686bb8abb5243f5df0b4276b7d81 Mon Sep 17 00:00:00 2001 From: Lars Bogner Date: Sat, 5 Jun 2021 11:54:53 +0200 Subject: [PATCH] Finished Informatik so far. --- Informatik/Informatik.md | 13 +++++++++++++ Informatik/Informatik.pdf | Bin 1441578 -> 1475569 bytes Informatik/assets/Addierer.png | Bin 0 -> 22917 bytes Informatik/assets/Volladdierer.png | Bin 0 -> 8019 bytes 4 files changed, 13 insertions(+) create mode 100644 Informatik/assets/Addierer.png create mode 100644 Informatik/assets/Volladdierer.png diff --git a/Informatik/Informatik.md b/Informatik/Informatik.md index 1f249a6..8d6cde9 100644 --- a/Informatik/Informatik.md +++ b/Informatik/Informatik.md @@ -226,5 +226,18 @@ In der Informatik wird sich auch grundlegend mit der informationstechnischen Log | XNOR-Gatter, `XNOR` | $\overline{A \oplus B}$ | ![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/IEC_XNOR_label.svg/125px-IEC_XNOR_label.svg.png) | +Aus diesen Logikverknüpfungen können Schaltungen bzw. boolesche Funktionen aufgebaut werden, welche anhand von booleschen Eingabewerten einen booleschen Ausgabewert erzeugen. Diese Schaltungen können beispielsweise mit den oben gezeigten Schaltsymbolen dargestellt werden. Zudem können alle möglichen Kombinationen in tabellarischer Form festgehalten werden. Dies nennt man eine Wahrheitstafel. Eine solche Wahrheitstafel kann zudem verwendet werden um die disjunktive Normalform herzuleiten. + +disjunktive Normalform +: Funktionsdarstellung einer booleschen Funktion, welche alle möglichen Kombinationen, welche zu einem wahren Ausgabewert führen disjunktiv verknüpft hat. Ein Beispiel wäre: $$({A}\wedge {B}\wedge \neg {C})\vee ({A}\wedge {B}\wedge {C})\vee (\neg{A}\wedge {B}\wedge {C})$$ + +Um mithilfe von Logikgattern eine Schaltung aufzubauen, welche zwei Binärzahlen addieren kann, wird wie folgt vorgegangen. Zunächst wird ein sogenannter Halbaddierer erstellt, welcher zwei Bits addieren kann. Die Summe der Bits wird dabei durch ein `XOR` realisiert und der entstehende Übertrag (vgl. schriftliche Addition) durch ein `AND`. Aus diesen Halbaddiereren kann nun ein Volladdierer erstellt werden, welcher 3 Bits addieren kann. Dies wird in der zugehörigen Abbildung dargestellt. Aus diesen Volladdierern kann abschließend eine Schaltung erstellt werden, welche eine beliebige Anzahl an Stellen addieren kann. Dies ist erneut in einer zugehörigen Abbildung zu erkennen. + +![Volladdierer aus Halbaddierern](assets/Volladdierer.png) + +![Addierer aus Volladdierern](assets/Addierer.png) + +Des Weiteren kann auch vergleichsweise einfach ein Subtrahierer gebaut werden. Hierfür wird als Differenz ein `XOR` verwendet und als Borger (Übetrag bei der Differenz) ein $\neg a \wedge b$. + diff --git a/Informatik/Informatik.pdf b/Informatik/Informatik.pdf index 645b66bd9c69696357fb62cea0f7476b36f1aba3..48270894c41e4233bbd56b94af0cacf26e3a43f8 100644 GIT binary patch delta 79810 zcmb5V2Q*z>w?2M|9->7T#p{%X&8<7iW!XS?o)R1$W1fFHH{GsOb?r=7;fdw;LjK0TazZ1VMBZ>V zs>J^3G zvj3((XUEQG&jC0WRtk~Aw3G!%j7VQ*g)z`rTASo>^U80!G3E|b8oc?vrN@cK@oa9A zi>%KxFgEYfi5@fIsaORtnuyDl`AzM#eF0@Oa1n3+?Tsf9+7lg)!?!uk{YDYti1hUZ zP1j>|QTx@O25N*Byo>}Xo&0`0L)^8H9>2a9oV?aQbG}oso~a@K;nnpS*gm^Q^|r7< zNb#odhP1A1-HUvAczqsK*&c%ufBAXl8E6 zGH)LbA;E8JkJbYR>K5u6fwT^DbB}6gQwl(6<;Y!K2srJnfjP`}(Odsg>W5Xf>&x6k z{NlDx70p@2n)3SQ=w3MexLT;iq(yH^viu+&NFVGJ zefBLwk!B^@wCR-=*`ZFA;0O2EXv! zw6!fGosg$JK1I2bMv7wIf0I5@5R>v{zZ_kdi({DBn?}|g->U~qtZkQF7Y?TFqo`Rw zkfviu_4rDPE2daM5?D7#Y@E>66-~WwH)Ha@KZ}i`XutFeY{kMu!|Ss-cf5~`LBJF7 zM-KPi+TGkRn*Y&^f}UZlcZ_9pI_D!KyCK6(lp2bOf97Aanpra{K5weHVz+6+v5MXH 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