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Entered-Variable K-Maps

  A generalization of the k-map method is to introduce variables into the k-map squares. These are called entered variable k-maps. This is useful for functions of large numbers of variabes, and can generally provide a clear way of representing Boolean functions.

An entered variable k-map is shown in Figure 30.


  
Figure 30: An entered variable k-map.
\begin{figure}
\begin{center}
\epsfig{file=images/diglogimg31.eps}\end{center}\end{figure}

Note the variable C in the top left square. It corresponds to

\begin{displaymath}\overline{A}.\overline{B} .C .
\end{displaymath}

It can be looped out with the 1, since 1=1+C, and we can loop out the two terms

\begin{displaymath}\overline{A}.\overline{B} .C \ \ {\rm and} \ \
{A}.\overline{B} .C
\end{displaymath}

to get

\begin{displaymath}\overline{B} .C .
\end{displaymath}

The remaining term

\begin{displaymath}{A}.\overline{B} .\overline{C}
\end{displaymath}

needs to be added to the cover, or more simply, just loop out the 1. The outcome is

\begin{displaymath}f = {A}.\overline{B} + \overline{B} .C .
\end{displaymath}

Think about this!

Figure 31 shows another EV k-map, with four entered variables C0, C1, C2, C3. Each of these terms are different and must be looped out individually to get

\begin{displaymath}f = \overline{A}.\overline{B}. C_0
+ \overline{A} .{B} .C_1
+ {A}.\overline{B} .C_2
+ {A}.{B} .C_3 .
\end{displaymath}


  
Figure 31: Another entered variable k-map.
\begin{figure}
\begin{center}
\epsfig{file=images/diglogimg32.eps}\end{center}\end{figure}


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