ITPEC FE Morning April 2023 Question 20
ITPEC FE Morning April 2023 — Question 20 of 80
Logic Circuit Equivalence — simplify a Boolean expression and match it to a circuit.
Given expression: Ā·B·C + A·C
Simplification:
- Factor out C: C · (Ā·B + A)
- Apply absorption law: Ā·B + A = A + B
- Result: C · (A + B)
Circuit structure:
- A, B → OR gate
- OR output + C → AND gate
Why not others:
- (a) — contains NAND/NOR inversions, wrong logic
- (b) — NAND input stage produces incorrect intermediate values
- (d) — overcomplicated with extra NAND gates, wrong output
Key rule: Always simplify the Boolean expression first using absorption (X̄·Y + X = X + Y) before matching to circuits — it reduces a 5-gate expression to 2 gates.
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