Convert the Boolean function F(A, B, C) = Σ(0, 1, 3, 5) to its simplified SOP…

Concept

A sum of minterms identifies exactly the input rows on which a Boolean function equals 1. In a Karnaugh map, adjacent 1-cells are grouped in the largest power-of-two blocks; each block removes the variable that changes within it. The minimal SOP is the smallest set of resulting product terms that covers every listed minterm.

Application

For F(A, B, C) = Σ(0, 1, 3, 5), write each minterm in binary and in canonical product form:

1. m0 = 000 = A'B'C'

2. m1 = 001 = A'B'C

3. m3 = 011 = A'BC

4. m5 = 101 = AB'C

The largest adjacent pairs on the K-map are:

• m0 and m1 differ only in C, giving A'B'.

• m1 and m3 differ only in B, giving A'C.

• m1 and m5 differ only in A, giving B'C.

The minterms m0, m3, and m5 each require one of these three implicants, so none can be removed. Therefore the minimal SOP is F = A'B' + A'C + B'C.

Cross-check

Truth-table evaluation of A'B' + A'C + B'C gives 1 exactly for ABC = 000, 001, 011, and 101, and 0 for the other four rows. Its on-set is therefore {0, 1, 3, 5}, which matches the given function.