ITPEC FE Morning April 2019 Question 23

A OR B — the AND gate's output is already covered by the OR gate beside it, so the final OR adds nothing.

• •Top gate (AND): A AND B
• •Bottom gate (OR): A OR B
• •Output gate (OR): (A AND B) OR (A OR B)

Whenever A AND B is 1, A OR B is 1 too, so ORing them gives A OR B (absorption: AB + A + B = A + B). The circuit outputs 0 only when A = B = 0.

Answer (c)

Why not others:

• •(a) — A AND B is only one branch; at A = 1, B = 0 it gives 0, but the circuit outputs 1
• •(b) — A AND (A OR B) absorbs to A; at A = 0, B = 1 it gives 0, but the circuit outputs 1
• •(d) — B AND (A OR B) absorbs to B; at A = 1, B = 0 it gives 0, but the circuit outputs 1

Key rule: Write each gate's output, combine them, then simplify with absorption: X + XY = X and X(X + Y) = X; one input where a candidate disagrees is enough to reject it.

Hardware · AI-written, may contain errors