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+\documentclass{article}
+\input kvmacros
+\sloppy
+\begin{document}
+\title{Typesetting Karnaugh Maps and Veitch Charts with \LaTeX}
+\author{Andreas W. Wieland\\eMail: \texttt{awwieland@gmx.de}}
+\date{January 7th, 2002}
+\maketitle
+
+
+\section{Abstract}
+
+Karnaugh maps and Veitch charts\footnote{In previous releases of this document
+ I referred to Karnaugh maps as Karnaugh-Veitch-Maps. This was definitely not
+ correct. Thanks to F.~M.~Brown for pointing this error out to me.} are used
+ to simplify logic equations. The drawing of them used to be a boring,
+ annoying and error-prone task. With the included macros this is no longer a
+ problem. They can typeset Karnaugh maps and Veitch charts with up to ten
+ variables, which is more than you might likely need. You only have to provide
+ a list of variable identifiers plus the function table of your logic
+ function(s). The macros also allow to mark the simplifications of your logic
+ function directly within a Karnaugh map or Veitch chart.
+
+\section{Introduction}
+
+Karnaugh maps and Veitch charts are used to simplify logic equations. They are
+map representations of logic functions, and in that they are equivalent. The
+difference between the two kinds of diagrams is the way in which the variables
+of the functions are located within the diagrams: ``The Karnaugh map \ldots{}
+displays a function's discriminants according to the reflected binary (Gray)
+code. The Veitch chart \ldots{} displays the discriminants in natural binary
+order.'' (F.~M.~Brown)
+
+However, the drawing of either kind of them used to be a boring, annoying and
+error-prone task. Since I had to typeset a 50+~page collection of exercises
+for a basic computer-science lecture with plenty of Karnaugh maps in it, I
+decided to write some macros that would do this task for me. Let us start
+first with an introduction on how to use these Macros:
+
+The first thing you have to do is to put the macro file \verb|kvmacros.tex|
+into a directory where \TeX{} will find it, i.e. you have to put it into a
+directory where your \texttt{TEXINPUTS} environment variable points to. You
+can then load them by typing
+\verb|\input kvmacros| somewhere in the preamble of your document.
+
+Suppose now you have a logic function~$f$ with the following function table:
+
+\begin{center}
+
+\begin{tabular}{lr}
+ \begin{tabular}[t]{r|cccc|c}
+Index&$a$&$b$&$c$&$d$&$f$\\
+\hline
+0&0&0&0&0&1\\
+1&0&0&0&1&1\\
+2&0&0&1&0&1\\
+3&0&0&1&1&0\\
+4&0&1&0&0&0\\
+5&0&1&0&1&1\\
+6&0&1&1&0&1\\
+7&0&1&1&1&0\\
+ \end{tabular}
+&
+ \begin{tabular}[t]{r|cccc|c}
+Index&$a$&$b$&$c$&$d$&$f$\\
+\hline
+8&1&0&0&0&0\\
+9&1&0&0&1&1\\
+10&1&0&1&0&1\\
+11&1&0&1&1&0\\
+12&1&1&0&0&0\\
+13&1&1&0&1&1\\
+14&1&1&1&0&1\\
+15&1&1&1&1&0\\
+ \end{tabular}
+\end{tabular}
+\end{center}
+
+This logic function can easily be put into a Karnaugh map by using the
+\verb|\karnaughmap|-macro\footnote{Users of older versions of the macro
+package will notice that the name has changed. Below you will find a
+discussion of the changes between versions.}. It has five parameters: The
+number of variables in the map, an identifier for the function, a list of
+variable identifiers for the variables, and the list of values of $f$ for
+each line in the function table. The variable identifiers in the third
+parameter are ordered from highest to lowest significance (the same way as in
+the function table, with $a$ having a significance of $2^3=8$ and $d$ having a
+significance of $2^0=1$). The list of values of $f$ was read from lowest to
+highest index. The fifth parameter remains empty in this example, it will be
+discussed below:
+
+\begin{verbatim}
+\karnaughmap{4}{f(a,b,c,d):}{abcd}{1110011001100110}{}
+\end{verbatim}
+
+This produces the following Karnaugh map, where the indices in the lower left
+corner of each box correspond to the indices in the function
+table:\footnote{The indices can easily be calculated from the variable values
+ in the function table, i.e. line 11: the index equals $a\cdot 2^3 + b\cdot
+ 2^2 + c \cdot 2^1 + d \cdot 2^0=1\cdot 8 + 0\cdot 4 + 1 \cdot 2 + 1 \cdot
+ 1=11$.}
+
+\begin{center}
+\karnaughmap{4}{f(a,b,c,d):}{abcd}{1110011001100110}{}
+\end{center}
+
+The macros work similar for Veitch charts:
+
+\begin{verbatim}
+\veitchchart{4}{f(a,b,c,d):}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+\begin{center}
+\veitchchart{4}{f(a,b,c,d):}{abcd}{0110011001100110}{}
+\end{center}
+
+Notice the difference in the variable location in the diagrams. In my opinion
+Karnaugh maps are much easier to use if you need to simplify a logic function;
+therefore Veitch charts will not be discussed any further in this
+document. Except otherwise noticed, the macros' syntax and functionality are
+exactly the same for Karnaugh maps and Veitch charts.
+
+The macros that read the variable list and the list of logic values
+(i.e. parameters \#3 and \#4) work
+recursively. Therefore, you have to take special care to supply the
+correct number of tokens to print: If you supply a list of variable
+identifiers or a list of logic values that contains fewer elements than needed
+the macros will cause error messages similar to the following:
+
+\begin{verbatim}
+! Argument of \kvgetonechar has an extra }.
+<inserted text>
+ \par
+l.201 }{}
+
+?
+\end{verbatim}
+
+On the contrary, if any of the two lists is longer than
+needed, \emph{you will not be notified!} Moreover, each entry has to be one
+character long, otherwise --- like a variable identifier enclosed in \$s ---
+you have to put it into braces:
+
+\begin{verbatim}
+\karnaughmap{4}{$f(a,b,c,d):$}{{$a$}{$b$}{$c$}{$d$}}{0110011001100110}{}
+\end{verbatim}
+
+This produces the following Karnaugh map:
+
+\begin{center}
+\karnaughmap{4}{$f(a,b,c,d):$}{{$a$}{$b$}{$c$}{$d$}}{0110011001100110}{}
+\end{center}
+
+\section{Marking simplifications}
+
+The already mentioned fifth parameter can be used if you want to draw
+something inside the Karnaugh map. For example this is useful if you want to
+show how you simplified a logic function:
+
+\begin{verbatim}
+\karnaughmap{4}{$f(a,b,c,d):$}{{$a$}{$b$}{$c$}{$d$}}%
+{0110011001100110}%
+{%
+\put(0,2){\oval(1.9,1.9)[r]}
+\put(4,2){\oval(1.9,1.9)[l]}
+\put(2,0){\oval(1.9,1.9)[t]}
+\put(2,4){\oval(1.9,1.9)[b]}
+}
+\end{verbatim}
+
+The corresponding Karnaugh map looks like this:
+
+\begin{center}
+\karnaughmap{4}{$f(a,b,c,d):$}{{$a$}{$b$}{$c$}{$d$}}%
+{0110011001100110}%
+{%
+\put(0,2){\oval(1.9,1.9)[r]}
+\put(4,2){\oval(1.9,1.9)[l]}
+\put(2,0){\oval(1.9,1.9)[t]}
+\put(2,4){\oval(1.9,1.9)[b]}
+}
+\end{center}
+
+You can use any of \LaTeX's graphics macros for this purpose. The Karnaugh map
+has its pivot point at the lower left point\footnote{This is not exactly true,
+but sufficient if you do not want to modify the macros.} and a unitlength that
+is equal to the length of a single box within the Karnaugh map. Sometimes you
+may find that the \verb|\oval|s that you want to draw inside a Karnaugh map are
+slightly shifted to the right. This occurs if you use the \verb|eepic|-Package
+in your document. In this case, make a copy of the \verb|eepic.sty| file,
+rename it to something like \verb|myeepic.sty| and comment out the definition
+of the \verb|\oval|-macro in your local copy. If you put this new
+\verb|myeepic.sty| file somewhere into your \TeX's search path so that \TeX{}
+can find it and you load it properly with e.g. \verb|\usepackage{myeepic}|,
+you shouldn't experience any more trouble.
+
+\section{Other features}
+
+There are some more features that you can use. Possibly the most important is
+that you can change the size of the diagrams by changing the size of the
+boxes within the map, simply by typing:
+
+\begin{verbatim}
+\kvunitlength=15mm
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+This results in the following Karnaugh map. The setting of the
+\verb|\kvunitlength| remains active until you change it again;\footnote{Or, of
+ course, until you leave the group in which you redefined the value. This
+ applies to all changeable parameters and macro definitions in this section!}
+the default \verb|\kvunitlength| is 8\,mm:
+
+\begin{center}
+\kvunitlength=15mm
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{center}
+
+Another feature is that you can switch off the indices inside the map by
+typing:
+
+\begin{verbatim}
+\kvnoindex
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+\begin{center}
+\kvunitlength=8mm
+\kvnoindex
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{center}
+
+This setting also remains active until you switch indexing on again using the
+\verb|\kvindex|-macro:
+
+\begin{verbatim}
+\kvindex
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+\begin{center}
+\kvindex
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{center}
+
+Usually, the font size of the map's contents and indices should be
+suitable (the defaults are \verb|\tiny| for \verb|\kvindexsize| and
+\verb|\normalsize| for \verb|\kvcontentsize|). If you want to change them, you
+can do this by redefining the \verb|\kvcontentsize|- and
+\verb|\kvindexsize|-macros (Preferably, you should do this in the preamble of
+your document):
+
+\begin{verbatim}
+\renewcommand\kvindexsize{\footnotesize}
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+\begin{center}
+\renewcommand\kvindexsize{\footnotesize}
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{center}
+
+In the same way you can also change the font family (Although I doubt that
+this is sensible):
+
+\begin{verbatim}
+\renewcommand\kvindexsize{\footnotesize\it}
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{verbatim}
+
+\begin{center}
+\renewcommand\kvindexsize{\footnotesize\it}
+\karnaughmap{4}{$f:$}{abcd}{0110011001100110}{}
+\end{center}
+
+
+These macros are named \verb|\kvfoo|, because they work both for Karnaugh maps
+and Veitch charts.
+
+\section{If you use an older version of the macros\ldots}
+
+\ldots{} you will certainly have noticed a number of changes. The most
+important one is that I have changed the name of the macro that draws Karnaugh
+maps from \verb|\kvmap| to \verb|\karnaughmap|. I suggest that you use the new
+name in documents that you newly create. However, I introduced an alias so
+that the old macro name still works:
+
+\begin{verbatim}
+\def\kvmap{\karnaughmap}
+\end{verbatim}
+
+Also, in some older versions tokens in the variable list or function table
+that were longer than one character had to be enclosed in \emph{double} braces
+(If you have used any of these versions you will certainly remember this
+annoying feature). This is no longer necessary --- however, it does no
+harm.
+
+If you need to know more about the exact changes, please consult the revision
+history in \verb|kvmacros.tex|.
+
+\section{Final remarks}
+
+This is all you need to know about the usage of my macros. I have tried them
+out and I haven't yet found any serious bugs, but I'm pretty sure there are
+plenty. In this case, or if you have comments or suggestions, please send me
+an eMail. Anyway, I would very much appreciate if you would notify me when you
+use my macros; I would like to know if they are of any use to somebody.
+
+The maximum size map I could produce was a Karnaugh map with 10~variables;
+with bigger maps I only exceeded \TeX's main memory. This is due to the
+macros' recursive algorithm. Quite likely you will exceed \TeX's capacity with
+even smaller maps if they occur in large documents, but I think no~one in his
+right mind will ever use Karnaugh maps of more than 6\,variables, so I didn't
+care about this problem.
+
+
+\section{More examples}
+
+Below I have given some more examples of Karnaugh maps produced with my
+macros:
+
+\begin{verbatim}
+\karnaughmap{1}{}{a}{01}{}
+
+\karnaughmap{2}{$f:$}{{$a$}{$b$}}{0110}{}
+
+\karnaughmap{3}{$f:$}{{$a$}{$b$}{$c$}}{01100110}{}
+
+\karnaughmap{4}{$f:$}{{$a$}{$b$}{$c$}{$d$}}{0110011001100110}{}
+
+\karnaughmap{4}{$f:$}{abcd}{abcdefghijklmnop}{}
+
+\karnaughmap{5}{$f:$}{{$a$}{$b$}{$c$}{$d$}{$e$}}%
+{0123456789abcdef0123456789abcdef}{}
+
+\karnaughmap{6}{$f_i^t:$}{abcdef}%
+{0123456789{10}{11}{12}{13}{14}{15}%
+{16}{17}{18}{19}{20}{21}{22}{23}%
+{24}{25}{26}{27}{28}{29}{30}{31}%
+{32}{33}{34}{35}{36}{37}{38}{39}%
+{40}{41}{42}{43}{44}{45}{46}{47}%
+{48}{49}{50}{51}{52}{53}{54}{55}%
+{56}{57}{58}{59}{60}{61}{62}{63}}{}%
+
+\kvunitlength=6mm
+\kvnoindex
+\karnaughmap{8}{$q_2^4:$}{{$a$}{$b$}{$c$}{$d$}{$e$}%
+{$f$}{$g$}{$h$}}{%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+}{}
+\kvunitlength=8mm
+\kvindex
+\end{verbatim}
+
+\begin{flushleft}
+\karnaughmap{1}{}{a}{01}{}
+
+\karnaughmap{2}{$f:$}{{$a$}{$b$}}{0110}{}
+
+\karnaughmap{3}{$f:$}{{$a$}{$b$}{$c$}}{01100110}{}
+
+\karnaughmap{4}{$f:$}{{$a$}{$b$}{$c$}{$d$}}{0110011001100110}{}
+
+\karnaughmap{4}{$f:$}{abcd}{abcdefghijklmnop}{}
+
+\karnaughmap{5}{$f:$}{{$a$}{$b$}{$c$}{$d$}{$e$}}%
+{0123456789abcdef0123456789abcdef}{}
+
+\karnaughmap{6}{$f_i^t:$}{abcdef}%
+{0123456789{10}{11}{12}{13}{14}{15}%
+{16}{17}{18}{19}{20}{21}{22}{23}%
+{24}{25}{26}{27}{28}{29}{30}{31}%
+{32}{33}{34}{35}{36}{37}{38}{39}%
+{40}{41}{42}{43}{44}{45}{46}{47}%
+{48}{49}{50}{51}{52}{53}{54}{55}%
+{56}{57}{58}{59}{60}{61}{62}{63}}{}%
+
+
+\kvunitlength=6mm
+\kvnoindex
+\karnaughmap{8}{$q_2^4:$}{{$a$}{$b$}{$c$}{$d$}{$e$}%
+{$f$}{$g$}{$h$}}{%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+0011001111001100%
+}{}
+\kvunitlength=8mm
+\kvindex
+\end{flushleft}
+
+\section{Sourcecode}
+
+Here now you will find the current sourcecode of my macros. I should have
+commented it more extensively, but failed due to lack of time. Sorry.
+
+\small
+\begin{verbatim}
+%% This is file `kvmacros.tex',
+%% Version of January 7th, 2002
+%%
+%% Copyright (C) 1998-2002 by Andreas W. Wieland, awwieland@gmx.de
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License distributed from CTAN
+%% archives in directory macros/latex/base/lppl.txt; either
+%% version 1 of the License, or (at your option) any later version,
+%% with `The Program' referring to the software `kvmacros.tex' and its
+%% accompanying documentation and `The Copyright Holder' referring to the
+%% person Andreas W. Wieland.
+%%
+%%
+%%
+%% IMPORTANT NOTICE:
+%%
+%% For error reports, comments or suggestions in case of UNCHANGED
+%% versions send mail to:
+%% awwieland@gmx.de
+%%
+%% Anyway, if you use my macros, send me an eMail, too. I would like to know
+%% if they are useful to somebody out there.
+%%
+%% Please do not request updates from me directly. Distribution is
+%% done through Mail-Servers and TeX organizations.
+%%
+%% You are allowed to distribute this file under the condition that
+%% it is distributed together with `kvdoc.tex', `kvdoc.dvi' and `kvdoc.ps'.
+%%
+%% If you receive this file alone from someone, complain!
+%%
+\typeout{}
+\typeout{Macros for typesetting Karnaugh maps and Veitch charts}
+\typeout{Version of January 7th, 2002}
+\typeout{by Andreas W. Wieland, awwieland@gmx.de}
+\typeout{}
+%%
+%% Change History:
+%% August 04th, 1998: Original Version
+%%
+%% August 19th, 1998: Minor changes to make the lines within the maps look
+%% better, also moved the variable identifiers from the right to the left and
+%% added an identifier for the logic function; since then \kvmap has 5
+%% instead of 4 parameters. I also included the documentation in an additional
+%% Postscript-file.
+%%
+%% September 23rd, 1998: Fixed the problem with double braces by introducing
+%% the \compdummy and \ende macros in the \ifx-comparisons (see below):
+%% The parameters that are longer than one character do not have to be
+%% enclosed in double braces any longer --- single braces are
+%% sufficient. However, double braces will still be processed correctly.
+%%
+%% May 19th, 1999: Changed the documentation (which was months overdue) after
+%% F. M. Brown pointed me to the incorrectness of the term
+%% "Karnaugh-Veitch-map". Actually, the macros itself haven't
+%% changed. Probably I should introduce macros for typesetting Veitch charts
+%% as well (which would be a minor task). This version was actually never
+%% released.
+%%
+%% May 25th, 1999: Introduced macros for Veitch charts
+%% (\veitchfoo) and renamed the macros that are solely related to
+%% Karnaugh maps from \kvfoo to \karnaughfoo. Introduced aliases for those
+%% macros that are user-callable to maintain compatibility with older versions:
+%% \kvmap -> \karnaughmap. However, \kvindex, \kvnoindex and \kvunitlength
+%% haven't changed their names as they are related to both Karnaugh maps and
+%% Veitch charts. Changed the (plain stupid) algorithm that processes the
+%% variable-length arguments so that it takes much less time to produce large
+%% maps. Several macros so became redundant and are no longer included. Also I
+%% introduced \kvindexsize and \kvcontentsize to adjust the font size of the
+%% indices and the contents of a diagram. They default to \tiny and
+%% \normalsize.
+%%
+%% January 17th, 2001: Changed the eMail-address in the macro file and the
+%% accompanying documentation and made minor changes to the documentation.
+%%
+%% January 7th, 2002: Exchanged the \xdef to \gdef in the definition of
+%% \kvargumentstring and \kvgetonechar so that things like {\textbf 1} in the
+%% argumentlist of \karnaughmap do not cause error messages any longer.
+%% Thanks to Michal Medveck{\'y} for pointing me to this error.
+%%
+%%
+%%
+%% We need a fixed dimension for a single field in a Karnaugh map:
+%%
+\newdimen\kvunitlength
+\kvunitlength=8mm
+%%
+%% We need a default font size for the indices:
+%%
+\newcommand{\kvindexsize}{\tiny}
+%%
+%% And we need a default size for the contents and variable identifiers:
+%%
+\newcommand{\kvcontentsize}{\normalsize}
+%%
+%% First, we have to introduce some counters:
+%%
+%% \kvrecursiondepth is used to control the recursion of the
+%% \karnaughmakemap- and \veitchmakechart-macro.
+%%
+\newcount\kvrecursiondepth
+%%
+%% The \kvindexcounter is needed for the indices in the fields of the
+%% diagrams.
+%%
+\newcount\kvindexcounter
+%%
+%% \kvxsize and \kvysize store the dimensions of an entire diagram.
+%%
+\newcount\kvxsize
+\newcount\kvysize
+%%
+%% Some counters are necessary to compute the marks for the variable
+%% identifiers:
+%%
+\newcount\kvvarno
+\newcount\kvxvarno
+\newcount\kvyvarno
+\newcount\kvmarkstart
+\newcount\kvmarklength
+\newcount\kvmarknum
+\newcount\kvmarkmove
+%%
+%% And we need a savebox to store the variable marks:
+%%
+\newsavebox\kvsavebox
+%%
+%% Single fields in a diagram should be indexed, which makes the map easier to
+%% use. This is the default. If you don't want indices, simply call
+%% \kvnoindex. If you want indices back, call \kvindex:
+%%
+\def\kvnoindex{%
+\def\kvcurrentindex{}}
+%%
+\def\kvindex{%
+\def\kvcurrentindex{%
+\the\kvindexcounter\global\advance\kvindexcounter by 1}%
+}
+%%
+\kvindex
+%%
+%% We need a macro that computes the powers of two:
+%%
+\def\kvpoweroftwo#1#2{% Computes #1=2^#2, both of which have to be counters
+{\ifnum#2>0
+\global\multiply#1 by 2
+\advance#2 by -1
+\kvpoweroftwo{#1}{#2}
+\fi}}
+%%
+%% The macros \kvargumentstring, \kvgetchar and \kvgetonechar are needed to
+%% process the variabe-length parameters in \karnaughmap and \veitchchart:
+%%
+\def\kvargumentstring#1{\gdef\kvdummystring{#1{}\noexpand\end}}
+%%
+\def\kvgetchar{\expandafter\kvgetonechar\kvdummystring}
+%%
+\def\kvgetonechar#1#2\end{{#1}\gdef\kvdummystring{#2\noexpand\end}}%
+%%
+%% The Macro \karnaughmakemap calls itself recursively until the parameter #1
+%% equals 1, whereupon it returns a single token from the list of arguments,
+%% enclosed in a \makebox plus the index (if enabled) in a smaller \makebox:
+%%
+\def\karnaughmakemap#1#2{{%
+\kvrecursiondepth=\number#1
+\ifnum\kvrecursiondepth>1
+\divide\kvrecursiondepth by 2
+\unitlength=\kvunitlength
+\multiply\unitlength by \kvrecursiondepth
+%%
+\ifcase#2
+%%
+%% The parameter #2 of \karnaughmakemap is needed because the inner Karnaugh
+%% maps need to be mirrored. This is achieved by the following case-statement,
+%% which orders the inner Karnaugh maps properly:
+%%
+%% Case 0: top-left Karnaugh map
+\begin{picture}(2,2)%
+\put(0,1){\karnaughmakemap{\kvrecursiondepth}{0}}%
+\put(1,1){\karnaughmakemap{\kvrecursiondepth}{1}}%
+\put(0,0){\karnaughmakemap{\kvrecursiondepth}{2}}%
+\put(1,0){\karnaughmakemap{\kvrecursiondepth}{3}}%
+\end{picture}%
+\or
+%% Case 1: top-right Karnaugh map
+\begin{picture}(2,2)%
+\put(1,1){\karnaughmakemap{\kvrecursiondepth}{1}}%
+\put(0,1){\karnaughmakemap{\kvrecursiondepth}{0}}%
+\put(1,0){\karnaughmakemap{\kvrecursiondepth}{3}}%
+\put(0,0){\karnaughmakemap{\kvrecursiondepth}{2}}%
+\end{picture}%
+\or
+%% Case 2: bottom-left Karnaugh map
+\begin{picture}(2,2)%
+\put(0,0){\karnaughmakemap{\kvrecursiondepth}{2}}%
+\put(1,0){\karnaughmakemap{\kvrecursiondepth}{3}}%
+\put(0,1){\karnaughmakemap{\kvrecursiondepth}{0}}%
+\put(1,1){\karnaughmakemap{\kvrecursiondepth}{1}}%
+\end{picture}%
+\or
+%% Case 3: bottom-right Karnaugh map
+\begin{picture}(2,2)%
+\put(1,0){\karnaughmakemap{\kvrecursiondepth}{3}}%
+\put(0,0){\karnaughmakemap{\kvrecursiondepth}{2}}%
+\put(1,1){\karnaughmakemap{\kvrecursiondepth}{1}}%
+\put(0,1){\karnaughmakemap{\kvrecursiondepth}{0}}%
+\end{picture}%
+\fi
+\else
+\unitlength=\kvunitlength
+\begin{picture}(1,1)
+\put(0,0){\makebox(1,1){\kvcontentsize\kvgetchar}}%
+\put(0.05,0.05){\makebox(0.9,0.9)[bl]{\kvindexsize\kvcurrentindex}}%
+\end{picture}
+\fi}}%
+%%
+%% \karnaughmaketopmark typesets the variable marks of a Karnaugh map that are
+%% located on top of the diagram:
+%%
+\def\karnaughmaketopmark{%
+ \unitlength\kvunitlength
+ \begin{picture}(\kvxsize,1)
+ \kvmarkstart=1
+ \kvpoweroftwo{\kvmarkstart}{\kvxvarno} % \kvymarkstart is the start
+ % position for the \multiput
+ \kvmarklength=\kvmarkstart
+ \multiply\kvmarklength by 2 % \kvmarklength is the length of a mark
+ \kvmarkmove=\kvmarkstart
+ \multiply\kvmarkmove by 4 % This is the move distance for the \multiput.
+ \kvmarknum=\kvxsize
+ \divide\kvmarknum by \kvmarkmove % This is the number of repetitions for
+ % the \multiput.
+ %The highest-order variable mark needs a special treatment:
+ \ifnum\kvmarknum=0\kvmarknum=1\divide\kvmarklength by 2\fi
+ \savebox\kvsavebox(\kvmarklength,1){%
+ \begin{picture}(\kvmarklength,1)
+ \put(0,0.3){\makebox(\kvmarklength,0.7){\kvcontentsize\kvgetchar}}
+ \put(0,0.1){\line(0,1){0.4}}
+ \put(\kvmarklength,0.1){\line(0,1){0.4}}
+ \put(0,0.3){\line(1,0){\kvmarklength}}
+ \end{picture}}
+ \multiput(\kvmarkstart,0)(\kvmarkmove,0){\kvmarknum}{\usebox\kvsavebox}
+ \end{picture}
+}
+%%
+%% \karnaughmakeleftmark typesets the variable marks of a Karnaugh map that are
+%% located on the left of the diagram:
+%%
+\def\karnaughmakeleftmark{%
+ \unitlength\kvunitlength
+ \begin{picture}(-1,\kvysize)(0,-\kvysize)
+ \kvmarkstart=1
+ \kvpoweroftwo{\kvmarkstart}{\kvyvarno} % \kvmarkstart is the start
+ % position for the \multiput
+ \kvmarklength=\kvmarkstart
+ \multiply\kvmarklength by 2 % \kvmarklength is the length of a mark
+ \kvmarkmove=\kvmarkstart
+ \multiply\kvmarkmove by 4 % This now is the move distance for the
+ % \multiput.
+ \kvmarknum=\kvysize
+ \divide\kvmarknum by \kvmarkmove % This now is the number of
+ % repetitions for the \multiput.
+ %The highest-order variable mark needs a special treatment:
+ \ifnum\kvmarknum=0\kvmarknum=1\divide\kvmarklength by 2\fi
+ \advance\kvmarkstart by \kvmarklength
+ \savebox\kvsavebox(1,\kvmarklength){%
+ \begin{picture}(1,\kvmarklength)
+ \put(-0.3,0){\makebox(-0.7,\kvmarklength){\kvcontentsize\kvgetchar}}
+ \put(-0.1,0){\line(-1,0){0.4}}
+ \put(-0.1,\kvmarklength){\line(-1,0){0.4}}
+ \put(-0.3,0){\line(0,1){\kvmarklength}}
+ \end{picture}}
+ \multiput(0,-\kvmarkstart)(0,-\kvmarkmove){\kvmarknum}{\usebox\kvsavebox}
+ \end{picture}
+}
+%% \karnaughmakemarks calls \karnaughmaketopmark or \karnaughmakeleftmark
+%% depending on whether \kvvarno is odd or even.
+%%
+\def\karnaughmakemarks{%
+\ifnum\kvvarno>0
+ \let\next=\karnaughmakemarks
+ \ifodd\kvvarno % We have to make a mark at the top
+ \advance\kvxvarno by -1
+ \put(0,\kvxvarno){\karnaughmaketopmark}
+ \else % We have to make a mark at the left
+ \advance\kvyvarno by -1
+ \put(-\kvyvarno,-\kvysize){\karnaughmakeleftmark}
+ \fi
+ \advance\kvvarno by -1
+\else
+ \let\next=\relax
+\fi
+\next
+}
+%%
+%% \karnaughmap is the macro that a user calls if he wants to draw a
+%% Karnaugh map:
+%%
+\def\karnaughmap#1#2#3#4#5{%
+%%
+%% #1 is the number of variables in the Karnaugh map
+%% #2 is the identifier of the function
+%% #3 is the list of identifiers of those variables
+%% #4 is the list of tokens that have to be written into the map
+%% #5 is something that you want to draw inside the Karnaugh map
+%%
+\kvvarno=#1 % \kvvarno is the total number of variables
+\kvyvarno=#1 % \kvyvarno is the number of variable marks at the left
+\divide\kvyvarno by 2
+\kvxvarno=#1 % \kvxvarno is the number of variable marks on top
+\advance\kvxvarno by -\kvyvarno
+\kvxsize=1
+\kvpoweroftwo{\kvxsize}{\kvxvarno}
+\kvysize=1
+\kvpoweroftwo{\kvysize}{\kvyvarno}
+\advance\kvxsize by \kvyvarno
+\advance\kvxvarno by \kvysize
+\unitlength\kvunitlength
+\begin{picture}(\kvxsize,\kvxvarno)(-\kvyvarno,-\kvysize)
+\advance\kvxsize by -\kvyvarno
+\advance\kvxvarno by -\kvysize
+\put(0,-\kvysize){%
+\begin{picture}(\kvxsize,\kvysize)
+\multiput(0,0)(0,1){\kvysize}{\line(1,0){\kvxsize}}
+\multiput(0,0)(1,0){\kvxsize}{\line(0,1){\kvysize}}
+\put(0,\kvysize){\line(1,0){\kvxsize}}
+\put(\kvxsize,0){\line(0,1){\kvysize}}
+#5
+\end{picture}}
+\put(-\kvyvarno,0){\makebox(\kvyvarno,\kvxvarno){#2}}
+\kvindexcounter=0
+\kvargumentstring{#4}
+\put(0,-\kvysize){\karnaughmakemap{\kvysize}{0}}
+\ifodd\kvvarno
+{\divide\kvxsize by 2
+\put(\kvxsize,-\kvysize){\karnaughmakemap{\kvysize}{1}}}
+\fi
+\kvargumentstring{#3}
+\karnaughmakemarks
+%%
+\end{picture}
+}%
+%%
+%% The definition of \kvmap is necessary to maintain compatibility with older
+%% versions of this macro package:
+%%
+\def\kvmap{\karnaughmap}%
+%%
+%%
+%% The Macro \veitchmakechart calls itself recursively until the parameter #1
+%% equals 1, whereupon it returns a single token from the list of arguments,
+%% enclosed in a \makebox plus the index (if enabled) in a smaller \makebox:
+%%
+\def\veitchmakechart#1{{%
+\kvrecursiondepth=\number#1
+\ifnum\kvrecursiondepth>1
+\divide\kvrecursiondepth by 2
+\unitlength=\kvunitlength
+\multiply\unitlength by \kvrecursiondepth
+%%
+\begin{picture}(2,2)%
+\put(0,1){\veitchmakechart{\kvrecursiondepth}}%
+\put(1,1){\veitchmakechart{\kvrecursiondepth}}%
+\put(0,0){\veitchmakechart{\kvrecursiondepth}}%
+\put(1,0){\veitchmakechart{\kvrecursiondepth}}%
+\end{picture}%
+\else
+\unitlength=\kvunitlength
+\begin{picture}(1,1)
+\put(0,0){\makebox(1,1){\kvcontentsize\kvgetchar}}%
+\put(0.05,0.05){\makebox(0.9,0.9)[bl]{\kvindexsize\kvcurrentindex}}%
+\end{picture}
+\fi}}%
+%%
+\def\veitchmaketopmark{%
+ \unitlength\kvunitlength
+ \begin{picture}(\kvxsize,1)
+ \kvmarkstart=1
+ \kvpoweroftwo{\kvmarkstart}{\kvxvarno} % \kvymarkstart is the start
+ % position for the \multiput
+ \kvmarklength=\kvmarkstart % \kvmarklength is the length of a mark
+ \kvmarkmove=\kvmarkstart
+ \multiply\kvmarkmove by 2 % This is the move distance for the \multiput.
+ \kvmarknum=\kvxsize
+ \divide\kvmarknum by \kvmarkmove % This is the number of repetitions for
+ % the \multiput.
+ \savebox\kvsavebox(\kvmarklength,1){%
+ \begin{picture}(\kvmarklength,1)
+ \put(0,0.3){\makebox(\kvmarklength,0.7){\kvcontentsize\kvgetchar}}
+ \put(0,0.1){\line(0,1){0.4}}
+ \put(\kvmarklength,0.1){\line(0,1){0.4}}
+ \put(0,0.3){\line(1,0){\kvmarklength}}
+ \end{picture}}
+ \multiput(\kvmarkstart,0)(\kvmarkmove,0){\kvmarknum}{\usebox\kvsavebox}
+ \end{picture}
+}
+%%
+\def\veitchmakeleftmark{%
+ \unitlength\kvunitlength
+ \begin{picture}(-1,\kvysize)(0,-\kvysize)
+ \kvmarkstart=1
+ \kvpoweroftwo{\kvmarkstart}{\kvyvarno} % \kvmarkstart is the start
+ % position for the \multiput
+ \kvmarklength=\kvmarkstart
+ \kvmarkmove=\kvmarkstart
+ \multiply\kvmarkmove by 2 % This now is the move distance for the \multiput.
+ \kvmarknum=\kvysize
+ \divide\kvmarknum by \kvmarkmove % This now is the number of
+ % repetitions for the \multiput.
+ \advance\kvmarkstart by \kvmarklength
+ \savebox\kvsavebox(1,\kvmarklength){%
+ \begin{picture}(1,\kvmarklength)
+ \put(-0.3,0){\makebox(-0.7,\kvmarklength){\kvcontentsize\kvgetchar}}
+ \put(-0.1,0){\line(-1,0){0.4}}
+ \put(-0.1,\kvmarklength){\line(-1,0){0.4}}
+ \put(-0.3,0){\line(0,1){\kvmarklength}}
+ \end{picture}}
+ \multiput(0,-\kvmarkstart)(0,-\kvmarkmove){\kvmarknum}{\usebox\kvsavebox}
+ \end{picture}
+}
+%%
+\def\veitchmakemarks{%
+\ifnum\kvvarno>0
+ \let\next=\veitchmakemarks
+ \ifodd\kvvarno % We have to make a mark at the top
+ \advance\kvxvarno by -1
+ \put(0,\kvxvarno){\veitchmaketopmark}
+ \else % We have to make a mark at the left
+ \advance\kvyvarno by -1
+ \put(-\kvyvarno,-\kvysize){\veitchmakeleftmark}
+ \fi
+ \advance\kvvarno by -1
+\else
+ \let\next=\relax
+\fi
+\next
+}
+%%
+\def\veitchchart#1#2#3#4#5{%
+%%
+%% #1 is the number of variables in the Veitch chart
+%% #2 is the identifier of the function
+%% #3 is the list of identifiers of those variables
+%% #4 is the list of tokens that have to be written into the chart
+%% #5 is something that you want to draw inside the Veitch chart
+%%
+\kvvarno=#1 % \kvvarno is the total number of variables
+\kvyvarno=#1 % \kvyvarno is the number of variable marks at the left
+\divide\kvyvarno by 2
+\kvxvarno=#1 % \kvxvarno is the number of variable marks on top
+\advance\kvxvarno by -\kvyvarno
+\kvxsize=1
+\kvpoweroftwo{\kvxsize}{\kvxvarno}
+\kvysize=1
+\kvpoweroftwo{\kvysize}{\kvyvarno}
+\advance\kvxsize by \kvyvarno
+\advance\kvxvarno by \kvysize
+\unitlength\kvunitlength
+\begin{picture}(\kvxsize,\kvxvarno)(-\kvyvarno,-\kvysize)
+\advance\kvxsize by -\kvyvarno
+\advance\kvxvarno by -\kvysize
+\put(0,-\kvysize){%
+\begin{picture}(\kvxsize,\kvysize)
+\multiput(0,0)(0,1){\kvysize}{\line(1,0){\kvxsize}}
+\multiput(0,0)(1,0){\kvxsize}{\line(0,1){\kvysize}}
+\put(0,\kvysize){\line(1,0){\kvxsize}}
+\put(\kvxsize,0){\line(0,1){\kvysize}}
+#5
+\end{picture}}
+\put(-\kvyvarno,0){\makebox(\kvyvarno,\kvxvarno){#2}}
+\kvindexcounter=0
+\kvargumentstring{#4}
+\put(0,-\kvysize){\veitchmakechart{\kvysize}}
+\ifodd\kvvarno
+{\divide\kvxsize by 2
+\put(\kvxsize,-\kvysize){\veitchmakechart{\kvysize}}}
+\fi
+\kvargumentstring{#3}
+\veitchmakemarks
+%%
+\end{picture}
+}%
+%%
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
+\end{verbatim}
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
+
+
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-20 16:16:41 +0000