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Karnaugh Maps 99

y=(Z&6&c) I(E&b&c) I (a&E&Z) I (a&6&c)
Sum-of-Products Expression

Figure 10-3. Example 3-input function

This is where Karnaugh Maps enter the game. The 1s assigned to the map’s
boxes represent the same minterms as the 1s in the truth table’s output column;
however, as the input values associated with each row and column in the map
differ by only one bit, any pair of horizontally or vertically adjacent boxes
corresponds to minterms that differ by only a single variable. Such pairs of
minterms can be grouped together and the variable that differs can be discarded
(Figure 10-4).

Truth Table
Yo0 01 11 10 Yo0 01 11 10

11

Figure 10-4. Karnaugh Map minimization
of example 3-input function

In the case of the horizontal group, input a is 0 for both boxes, input c is 1
for both boxes, and input b is 0 for one box and 1 for the other. Thus, for this
group, changing the value on b does not affect the value of the output. This
means that b is redundant and can be discarded from the equation representing
this group. Similarly, in the case of the vertical group, input a is 1 for both
boxes, input b is 0 for both boxes, and input c is 0 for one box and 1 for the
other. Thus, input c is redundant for this group and can be discarded.