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boole.tex
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boole.tex
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% coding:utf-8
%FOSAET, a LaTeX-Code for a electrical summary of basic electronics
%Copyright (C) 2013, Daniel Winz, Ervin Mazlagic
%This program is free software; you can redistribute it and/or
%modify it under the terms of the GNU General Public License
%as published by the Free Software Foundation; either version 2
%of the License, or (at your option) any later version.
%This program is distributed in the hope that it will be useful,
%but WITHOUT ANY WARRANTY; without even the implied warranty of
%MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
%GNU General Public License for more details.
%----------------------------------------
\section{Schreibweise logischer Funktionen}
\[ \text{ NOT }y = \neg y = \overline{y} \]
\[ x\text{ OR }y = x \lor y = x + y \]
\[ x\text{ AND }y = x \land y = x \cdot y \]
\[ x\text{ XOR }y = x \underline{\lor} y = x \oplus y \]
\section{Boolesche Algebra}
\[ \begin{array}{lllll} \overline{\overline{x}} = x &
x \land x = x &
x \land \overline{x} = 0 &
x \lor x = x &
x \lor \overline{x} = 1 \end{array} \]
\[ \begin{array}{llll} x \land 0 = 0 &
x \land 1 = x &
x \lor 0 = x &
x \lor 1 = 1 \end{array}\]
\[ \begin{array}{ll}
x \land y = y \land x &
x \lor y = y \lor x \\\\
\overline{x} \land \overline{y} = \overline{x \lor y} &
\overline{x} \lor \overline{y} = \overline{x \land y} \\\\
\overline{\overline{x} \land \overline{y}} = x \lor y &
\overline{\overline{x} \lor \overline{y}} = x \land y \\\\
x \land (x \lor y) = x & x \lor (x \land y) = x \\\\
x \land (\overline{x} \lor y) = x \land y &
x \lor (\overline{x} \land y) = x \lor y \\\\
(x \land y) \lor (\overline{x} \land y = y) &
(x \lor y) \land (\overline{x} \lor y = y) \\
\end{array} \]
\[ \]