In certain cases a function may be incompletely specified; that is, the output may be undefined for some of the input combinations. If the designer knows that certain input combinations will never occur, then the value assigned to the output for these combinations is irrelevant.
Alternatively, for some input combinations the designer may simply not care about the value on the output. In both cases, the designer can represent the output values associated with the relevant input combinations as question marks in the map (Figure 8).
Figure 8:
Karnaugh map for an
incompletely specified
function.
The ? characters indicate don't care states which can be considered to represent either 0 or 1 values at the designer's discretion. It should be noted that many electronics references use X characters to represent don't care states. Unfortunately, this may lead to confusion as design tools such as logic simulators use X characters to represent don't know states. Unless otherwise indicated, this book uses ? and X to represent don't care and don't know states respectively.