Don't Cares condition
Don't Cares condition:
Sometimes we do not care whether a 1 or 0 occurs for a certain set of inputs. It may be that those inputs will never occur so it makes no difference what the output is. For example, we might have a bcd (binary coded decimal) code which consists of 4 bits to encode the digits 0 (0000) through 9 (1001). The remaining codes (1010 through 1111) are not used. If we had a truth table for the prime numbers 0 through 9, it would be
The ds in the above stand for "don't care", we don't care whether a 1 or 0 is the value for that combination of inputs because (in this case) the inputs will never occur.
The circle made entirely of 1s corresponds to the expression a'd and the combined 1 and d circle (actually a combination of arcs) is b'c. Thus, if the disallowed input 1011 did occur, the output would be 1 but if the disallowed input 1100 occurs, its output would be 0. The minimized expression is p = a'd b'c
Notice that if we had ignored the ds and only made a circle around the 2 1s, the resulting expression would have been more complex, a'b'c instead of b'c.