TABLE OF CONTENTS A Karnaugh map, henceforth referred to as K-map, is a matrix of squares. In general, a Boolean expression with n variables can be represented by a K-map of 2 n squares where each square represents a row of an equivalent truth table. A K-map provides a very powerful method of reducing Boolean expressions to their simplest forms.
Figure 7.25 shows a two-variable K-map with four squares where each square represents one combination of the variables.
In figure 7.25,
square a represents the combination A=0 and B=0, that is, a ? AB
square b represents the combination A=0 and B=1, that is, b ? AB
square c represents the combination A=1 and B=0, that is, c ?A B
square d represents the combination A=1 and B=1, that is, d ?AB
For example, the Boolean expression C= AB+A B can be shown in a K-map as indicated in Figure 7.26 where the 1s denote the conditions for which the Boolean expression is true (logical 1).
For simplicity, we enter only 1 s l in the squares of a K-map and it is understood that all other empty squares contain 0s.
We can also derive a Boolean expression from a K-map. For example, from the K-map shown in Figure 7.27 we derive the Boolean expression Z= X
