Don't Care Conditions:
In some of the digital systems, some inputs are never supplied so no output is visible. We call such cases don't care conditions and they are depicted by X in the truth table as represented in Figure (c). Whenever we see an X in the truth table whereas encircling the 1s in the K-map to form the largest group, we may assume Xs as 1s. After this has been included in all of the groups, disregard the Xs in the truth tables by supposing them as 0s. For the case of Figure (c), the SOP equation after Karnaugh simplifications are Y = B.
(a) (b) (c)
Figure: (a) Overlapped Groups, (b) Rolling, and (b) Don't Care Conditions of K-maps