Incompletely Specified Functions
A switching function may be incompletely specified.
Some minterms are omitted, which are called don't-care minterms.
Don't cares arise in two ways:
- Certain input combinations never occur.
- Output is required to be 1 or 0 only for certain combinations.
Don't care minterms: di Don't care maxterms: Di
Example: f(A,B,C) has minterms m0, m3, and m7 and don't-cares d4 and d5.
- Minterm list is: f(A,B,C) = ?m(0,3,7) + d(4,5)
- Maxterm list is: f(A,B,C) = ?M(1,2,6)·D(4,5)
- f '(A,B,C) = ?m(1,2,6) + d(4,5) = ?M(0,3,7)·D(4,5)
- f (A,B,C)= A'B'C' + A'BC + ABC + d(AB'C' + AB'C)
= B'C' + BC (use d4 and omit d5)