Given the Boolean function

$F = (A + \overline{B}C)(\overline{A} + B + \overline{C}) + A\overline{B}C$,

(a) simplify $F$ to a minimal sum‑of‑products form, and (b) using only two‑input NAND gates, determine the minimum number of NAND gates required to implement the simplified function.

Question

Given the Boolean function

$F = (A + \overline{B}C)(\overline{A} + B + \overline{C}) + A\overline{B}C$,

(a) simplify $F$ to a minimal sum‑of‑products form, and (b) using only two‑input NAND gates, determine the minimum number of NAND gates required to implement the simplified function.

Accepted Answer

Simplified form: $F = AB + A\overline{C} + \overline{B}C$. Minimum NAND gates required: 14.

Neco 2022 Data Processing Question 39

Given the Boolean function \(F = (A + \overline{B}C)(\overline{A} + B + \overline{C}) + A\overline{B}C\), (a) simplify \(F\) to a minimal sum‑of‑products form, and (b) using only two‑input NAND gates, determine the minimum number of NAND gates required to implement the simplified function.

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