Define the Don't Care States - Simplifying K Maps?

The Truth table specifications for a logic function may not to include all possible combinations of the input binary digits for the input variables yet they may still be complete specifications of the logic function for the prescribed application. In these circumstances certain input combinations will not take place due to the nature of the application when the input combinations are irrelevant or cannot take place, the output states are in the Truth table and the K map are filled with an X and are referred to as don't care states.

When simplifying K maps with a don't care states, the contents of the undefined cells (1 or 0) are chosen according to preference. The aim is to extend group sizes thereby eliminating as many input variables from the simplified expression as possible. Only those X's that support in simplifying the function should be included in the groupings and No additional X's should be added that would result in additional terms in the expression.