Handling of Don't Care conditions (in SOP)

Rules for handling Don't Care conditions in simplification process:

1. Prepare the respective map depending upon the number of variables used in the function.
2. Put 1 on appropriate places for every min-term provided in the function.
3. Put a CROSS ( X ) on every min-term showing Don't Care condition.
4. Make pairs of 1's in the map. Consider the CROSSes also like a 1 in the map, since we Don't know whether that min-term is a 0 or a 1.
5. If any Don't Care min-term is left unpaired, leave it. No any evaluation is required for this unpaired min-term, as it is a Don't Care condition.
6. At last, deduce the expression simply like a normal K-map.

Notes:

• Don't Care condition is a significant issue in understanding and simplifying Boolean expressions. Since its name is pretty much descriptive, a Don't Care condition simply means that the machine is not sure about its output. On the same min-term, it can be 0 or 1.
• These conditions are marked as a cross ( X ) in the K-map, and are evaluated simply as other min-terms.
• Don't Care terms are feasible for evaluation but only as far as they contribute in making larger groups thereby improving the simplification.

Ex.   Simplify the following function in SOP form using K-map method.

Solution.