The Boolean function $G(A,B,C)$ is true for minterms 0, 2, 5, 7, i.e.

$$G = \Sigma m(0,2,5,7).$$

(a) Obtain a minimal product‑of‑sums (POS) expression for $G$.\n
(b) Using only 2‑input NAND gates, what is the minimum number of NAND gates required to implement the POS expression? Assume each NAND gate has a unit cost.

Question

The Boolean function $G(A,B,C)$ is true for minterms 0, 2, 5, 7, i.e.

$$G = \Sigma m(0,2,5,7).$$

(a) Obtain a minimal product‑of‑sums (POS) expression for $G$.\n
(b) Using only 2‑input NAND gates, what is the minimum number of NAND gates required to implement the POS expression? Assume each NAND gate has a unit cost.

Accepted Answer

Minimal POS: $(A + \overline{C})(\overline{A} + C)$. Minimum NAND gates: 6.

Neco 2022 Data Processing Question 44

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