Don't Care Condition

In some applications, the function is not specified for certain combinations of the variables. That is why they are called don't care conditions, as whatever may be its value 0 or 1, it does not make any effect. 

The "Don't care" condition are those in which we can use the blank cells of a K-map to make a group of the variables. To make a group of cells, we can use the "don't care" cells as either 0 or 1, and if required, we can also ignore that cell. They are denoted by 'X' in the K-Map cells.

This cross symbol represents an invalid combination

Main advantage of using don't care condition is that we can make large groups of variables, which results in more simplified expression. When the expression is simpler then it also reduces the number of logic gates used.

Example: Simplify the Boolean function F(A,B,C,D) = π(4,7,10,11,12,15) which has the don't-care conditions d(A,B,C,D)=  π(6,8)