From d61040041bf28cba6bc25f22bc06ee8184487855 Mon Sep 17 00:00:00 2001 From: Roger Wolf <roger.wolf@kit.edu> Date: Tue, 29 Oct 2024 11:44:45 +0100 Subject: [PATCH] adding files --- Schaltlogik/doc/Hinweise-Logik.md | 81 ++++++++++++++++++++++++++++++ Schaltlogik/figures/FPGA.odg | Bin 0 -> 3071471 bytes Schaltlogik/figures/FPGA.png | Bin 0 -> 960749 bytes 3 files changed, 81 insertions(+) create mode 100644 Schaltlogik/doc/Hinweise-Logik.md create mode 100644 Schaltlogik/figures/FPGA.odg create mode 100644 Schaltlogik/figures/FPGA.png diff --git a/Schaltlogik/doc/Hinweise-Logik.md b/Schaltlogik/doc/Hinweise-Logik.md new file mode 100644 index 0000000..279ea08 --- /dev/null +++ b/Schaltlogik/doc/Hinweise-Logik.md @@ -0,0 +1,81 @@ +# Hinweise für den Versuch Schaltlogik + +## Schaltung eines NOT- aus einem NOR-Gatter + +Die Wahrheitstafel für das **NOR-Gatter** ist +$$ +\begin{equation} +\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = \overline{A \lor B}} \\ + \hline + \mathbf{0} & \mathbf{0} & \mathbf{1} \\ + 0 & 1 & 0 \\ + 1 & 0 & 0 \\ + \mathbf{1} & \mathbf{1} & \mathbf{0} \\ +\end{array} +\end{equation} +$$ +Dieses lässt sich zu einem **NOT-Gatter für den Eingang A** reduzieren, indem man die Bedingung +$$ +\begin{equation*} +A=B +\end{equation*} +$$ +an den Eingängen A und B implementiert, wie aus den hervorgehobenen **Zeilen 1 und 4 der Wahrheitstafel in Gleichung (1)** zu erkennen ist. + +Man erhält das gleiche Ergebnis, für die Bedingung +$$ +\begin{equation} +\begin{split} +&\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = \overline{A \lor B}} \\ + \hline + \mathbf{0} & \mathbf{0} & \mathbf{1} \\ + 0 & 1 & 0 \\ + \mathbf{1} & \mathbf{0} & \mathbf{0} \\ + 1 & 1 & 0 \\ +\end{array} \\ +&\\ +&\text{mit: } \mathrm{B=0},\\ +\end{split} +\end{equation} +$$ +wie in den hervorgehobenen **Zeilen 1 und 3 in der Wahrheitstafel aus Gleichung (2)** zu sehen ist. + +## Schaltung eines NOT- aus einem NAND-Gatter + +Ähnliche Bedingungen kann man ableiten, um das NAND- zu einem NOT-Gatter zu reduzieren, wie in Gleichungen **(3)** gezeigt: +$$ +\begin{equation} +\begin{split} +&\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = \overline{A \land B}} \\ + \hline + \mathbf{0} & \mathbf{0} & \mathbf{1} \\ + 0 & 1 & 1 \\ + 1 & 0 & 1 \\ + \mathbf{1} & \mathbf{1} & \mathbf{0} \\ +\end{array}\\ +&\\ +&\text{mit: } \mathrm{A=B}\\ +&\\ +&\\ +&\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = \overline{A \land B}} \\ + \hline + 0 & 0 & 1 \\ + \mathrm{0} & \mathrm{1} & \mathrm{1} \\ + 1 & 0 & 1 \\ + \mathbf{1} & \mathbf{1} & \mathbf{0} \\ +\end{array}\\ +&\\ +&\text{mit: } \mathrm{B=1}.\\ +\end{split} +\end{equation} +$$ + + +# Navigation + +[Main](https://gitlab.kit.edu/kit/etp-lehre/p1-praktikum/students/-/tree/main/Schaltlogik) + diff --git a/Schaltlogik/figures/FPGA.odg b/Schaltlogik/figures/FPGA.odg new file mode 100644 index 0000000000000000000000000000000000000000..f429acf228ce4a04ad68e924b287f11864508ec3 GIT 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