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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 168.

  

Figure 168: An entered variable k-map.

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

$$\overline{A}.\overline{B} .C .$$

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

$$\overline{A}.\overline{B} .C \ \ {\rm and} \ \ {A}.\overline{B} .C$$

to get

$$\overline{B} .C .$$

The remaining term

$${A}.\overline{B} .\overline{C}$$

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

$$f = {A}.\overline{B} + \overline{B} .C .$$

Think about this!

Figure 169 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

$$f = \overline{A}.\overline{B}. C_0 + \overline{A} .{B} .C_1 + {A}.\overline{B} .C_2 + {A}.{B} .C_3 .$$

  

Figure 169: Another entered variable k-map.

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