File:Crossover nand.pdf
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Summary
| Description |
English: Crossover gadget for wires x and y, implemented as a planar circuit using ten nand gates. Using this gadget, every boolean circuit can be converted into an equivalent planar circuit, provided nand gates are allowed. Each wire is attached a colored label, corresponding to a column in a truth table. Circuitery inspired from Fig. 11 and 12 (p.14) of:
Richard Kaye (Mar 2000). "Minesweeper is NP-complete". The Mathematical Intelligencer 22: 9–15. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Planar SAT Crossover Gadget.png * File:Crossover xor.gif * File:Crossover nand.pdf * File:Crossover nand svg.svg |
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{{vector version available|new image name}}.
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LaTeX source code
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\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=135\unitlength,paperheight=65\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{135\unitlength}
\setlength{\textheight}{65\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
% colors
\definecolor{fWire} {rgb}{0.40,0.40,0.40}
\definecolor{fGate} {rgb}{0.00,0.00,0.00}
% signals
\definecolor{foIoI} {rgb}{0.70,0.00,0.00}
\definecolor{fooII} {rgb}{0.00,0.70,0.00}
\definecolor{fIIIo} {rgb}{0.00,0.00,0.70}
\definecolor{fIIoI} {rgb}{0.00,0.50,0.50}
\definecolor{fIoII} {rgb}{0.50,0.00,0.50}
\definecolor{foIIo} {rgb}{0.50,0.50,0.00}
\newcommand{\nand}{%
\put(0,-5){\line(0,1){10}}%
\put(0, 0){\oval(10,10)[r]}%
\put(5, 0){\circle*{2}}%
%\put(0, 3){\line(1,0){1}}%
%\put(0,-3){\line(1,0){1}}%
}
\newcommand{\vect}[1]{%
\textcolor{f#1}{$\scriptstyle #1$}%
}
\begin{document}
\begin{picture}(130,60)%
%\put(0,0){\makebox(0,0){$+$}}%
%\put(130,60){\makebox(0,0){$+$}}%
\thicklines%
% x,y input -->
\textcolor{fWire}{\put(5,15){\line(1,0){40}}}%
\textcolor{fWire}{\put(5,45){\line(1,0){40}}}%
\textcolor{fWire}{\put(20,15){\circle*{1}}}%
\textcolor{fWire}{\put(20,45){\circle*{1}}}%
\textcolor{fWire}{\put(20,15){\line(0,1){12}}}%
\textcolor{fWire}{\put(20,45){\line(0,-1){12}}}%
\textcolor{fWire}{\put(20,33){\line(1,0){ 5}}}%
\textcolor{fWire}{\put(20,27){\line(1,0){ 5}}}%
\textcolor{fWire}{\put(20,15){\line(0,-1){13}}}%
\textcolor{fWire}{\put(20,45){\line(0, 1){13}}}%
\textcolor{fWire}{\put(20, 2){\line(1,0){65}}}%
\textcolor{fWire}{\put(20,58){\line(1,0){65}}}%
% x|y -->
\textcolor{fWire}{\put(30,30){\line(1,0){5}}}%
\textcolor{fWire}{\put(35,30){\circle*{1}}}%
\textcolor{fWire}{\put(35,30){\line(0,-1){9}}}%
\textcolor{fWire}{\put(35,30){\line(0, 1){9}}}%
\textcolor{fWire}{\put(35,39){\line(1,0){10}}}%
\textcolor{fWire}{\put(35,21){\line(1,0){10}}}%
% (x|y)|y -->
\textcolor{fWire}{\put(50,18){\line(1,0){25}}}%
\textcolor{fWire}{\put(55,18){\circle*{1}}}%
\textcolor{fWire}{\put(75,18){\circle*{1}}}%
\textcolor{fWire}{\put(55,18){\line(0,1){9}}}%
\textcolor{fWire}{\put(55,27){\line(1,0){10}}}%
\textcolor{fWire}{\put(75,18){\line(0,1){3}}}%
\textcolor{fWire}{\put(75,18){\line(0,-1){10}}}%
\textcolor{fWire}{\put(75,21){\line(1,0){10}}}%
\textcolor{fWire}{\put(75,8){\line(1,0){10}}}%
% (x|y)|x -->
\textcolor{fWire}{\put(50,42){\line(1,0){25}}}%
\textcolor{fWire}{\put(55,42){\circle*{1}}}%
\textcolor{fWire}{\put(75,42){\circle*{1}}}%
\textcolor{fWire}{\put(55,42){\line(0,-1){9}}}%
\textcolor{fWire}{\put(55,33){\line(1,0){10}}}%
\textcolor{fWire}{\put(75,42){\line(0,-1){3}}}%
\textcolor{fWire}{\put(75,42){\line(0,1){10}}}%
\textcolor{fWire}{\put(75,39){\line(1,0){10}}}%
\textcolor{fWire}{\put(75,52){\line(1,0){10}}}%
% x+y -->
\textcolor{fWire}{\put(70,30){\line(1,0){5}}}%
\textcolor{fWire}{\put(75,30){\circle*{1}}}%
\textcolor{fWire}{\put(75,30){\line(0,-1){3}}}%
\textcolor{fWire}{\put(75,30){\line(0, 1){3}}}%
\textcolor{fWire}{\put(75,27){\line(1,0){10}}}%
\textcolor{fWire}{\put(75,33){\line(1,0){10}}}%
% --> nand for y
\textcolor{fWire}{\put(90,55){\line(1,0){5}}}%
\textcolor{fWire}{\put(90,36){\line(1,0){5}}}%
\textcolor{fWire}{\put(95,55){\line(0,-1){7}}}%
\textcolor{fWire}{\put(95,36){\line(0, 1){6}}}%
\textcolor{fWire}{\put(95,48){\line(1,0){10}}}%
\textcolor{fWire}{\put(95,42){\line(1,0){10}}}%
% --> nand for x
\textcolor{fWire}{\put(90, 5){\line(1,0){5}}}%
\textcolor{fWire}{\put(90,24){\line(1,0){5}}}%
\textcolor{fWire}{\put(95, 5){\line(0, 1){7}}}%
\textcolor{fWire}{\put(95,24){\line(0,-1){6}}}%
\textcolor{fWire}{\put(95,12){\line(1,0){10}}}%
\textcolor{fWire}{\put(95,18){\line(1,0){10}}}%
% --> y
\textcolor{fWire}{\put(110,45){\line(1,0){15}}}%
% --> x
\textcolor{fWire}{\put(110,15){\line(1,0){15}}}%
% inputs
\textcolor{fWire}{\put(5,15){\circle*{1}}}%
\put(3,15){\makebox(0,0)[r]{$y$}}%
\textcolor{fWire}{\put(5,45){\circle*{1}}}%
\put(3,45){\makebox(0,0)[r]{$x$}}%
%gates
\textcolor{fGate}{\put(25,30){\nand}}% x|y
%
\textcolor{fGate}{\put(45,18){\nand}}%
\textcolor{fGate}{\put(45,42){\nand}}%
%
\textcolor{fGate}{\put(65,30){\nand}}% x+y
%
\textcolor{fGate}{\put(85, 5){\nand}}%
\textcolor{fGate}{\put(85,24){\nand}}%
\textcolor{fGate}{\put(85,36){\nand}}%
\textcolor{fGate}{\put(85,55){\nand}}%
%
\textcolor{fGate}{\put(105,15){\nand}}% y out
\textcolor{fGate}{\put(105,45){\nand}}% x out
% outputs
\textcolor{fWire}{\put(125,15){\circle*{1}}}%
\put(127,15){\makebox(0,0)[l]{$x$}}%
\textcolor{fWire}{\put(125,45){\circle*{1}}}%
\put(127,45){\makebox(0,0)[l]{$y$}}%
% value vectors
\put( 19,14){\makebox(0,0)[tr]{\vect{oIoI}}}%
\put( 19,46){\makebox(0,0)[br]{\vect{ooII}}}%
\put( 36,30){\makebox(0,0)[l] {\vect{IIIo}}}%
\put( 56,17){\makebox(0,0)[tl]{\vect{IoII}}}%
\put( 56,43){\makebox(0,0)[bl]{\vect{IIoI}}}%
\put( 76,30){\makebox(0,0)[l] {\vect{oIIo}}}%
\put(96, 5){\makebox(0,0)[l] {\vect{IIIo}}}%
\put(96,24){\makebox(0,0)[l] {\vect{IIoI}}}%
\put(96,36){\makebox(0,0)[l] {\vect{IoII}}}%
\put(96,55){\makebox(0,0)[l] {\vect{IIIo}}}%
\put(124,46){\makebox(0,0)[br]{\vect{oIoI}}}%
\put(124,14){\makebox(0,0)[tr]{\vect{ooII}}}%
\end{picture}
\end{document}
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:28, 18 December 2022 |  | 795 × 383 (22 KB) | Jochen Burghardt | Uploaded own work with UploadWizard |
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