Digital Logic20755 marksNumerical: Sum of mintermsBoolean Functions
Express the Boolean function F = A+B'C in a sum of minterms.
Express the Boolean function F = A+B'C in a sum of minterms. [5]
- Boolean function: $F = A + B'C$ - Variables: $A, B, C$ (3 variables, so $2^3 = 8$ possible minterms) --- $$A = A(B+B')(C+C') = (AB + AB')(C+C')$$ $$= ABC + ABC' + AB'C + AB'C'$$ $$B'C = B'C(A+A') = AB'C + A'B'C$$ $$F = ABC + ABC' + AB'C + AB'C' + AB'C + A'B'C$$ The term $AB'C$ appears twice, so...