Given the Boolean function F(A, B, C) = Σ(0, 1, 2, 3, 5), what is its…

Concept

In a three-variable Boolean function, each minterm identifies one input combination for which the output is 1. In a Karnaugh map, grouping 2n adjacent 1s removes the n variables that change; the variables that stay constant form the product term. The SOP expression is the OR of product terms that together cover all required minterms.

Application

1. Place 1s in the three-variable Karnaugh map at minterms 0, 1, 2, 3, and 5.

2. The four adjacent cells m0, m1, m2, and m3 form a group. Here A = 0 remains constant while B and C vary, so this group gives A'.

3. The adjacent cells m1 and m5 form a pair. Here B = 0 and C = 1 remain constant while A varies, so this pair gives B'C.

4. OR the two implicants: F = A' + B'C.

Cross-check

A' covers minterms {0, 1, 2, 3}, and B'C covers {1, 5}. Their union is exactly {0, 1, 2, 3, 5}, with no extra minterm.

Contrast

• A'B' + AB' + AB + AC has the 1-set {0, 1, 4, 5, 6, 7}.

• A + B + C has the 1-set {1, 2, 3, 4, 5, 6, 7}.

• AB' + C' has the 1-set {0, 2, 4, 5, 6}.

• A' + B'C has the 1-set {0, 1, 2, 3, 5}.

Therefore, the simplified SOP expression is F = A' + B'C.