The Boolean function $F(A,B,C,D)$ is defined by the minterms

$$F = \Sigma m(1,3,4,6,9,11,12,14).$$

(a) Simplify $F$ to a minimal sum‑of‑products expression using a Karnaugh map.

(b) If each 2‑input AND, OR, and NOT gate costs 1 unit, determine the minimum total cost (in gate units) required to implement the simplified expression using only 2‑input gates.

Question

The Boolean function $F(A,B,C,D)$ is defined by the minterms

$$F = \Sigma m(1,3,4,6,9,11,12,14).$$

(a) Simplify $F$ to a minimal sum‑of‑products expression using a Karnaugh map.

(b) If each 2‑input AND, OR, and NOT gate costs 1 unit, determine the minimum total cost (in gate units) required to implement the simplified expression using only 2‑input gates.

Accepted Answer

Minimal SOP: $\overline{B}D + B\overline{D}$. Minimum cost: 5 gate units.

Neco 2022 Data Processing Question 42

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