ITPEC FE Morning April 2022 Question 21

XNOR using NOR gates — identify the circuit that implements Exclusive-NOR using only two-input NOR gates.

XNOR truth table:
- A=0, B=0 → 1
- A=0, B=1 → 0
- A=1, B=0 → 0
- A=1, B=1 → 1

How option (d) works:
- First level: NOR(A,A) = NOT A, NOR(B,B) = NOT B
- Second level: NOR(A, NOT B), NOR(NOT A, B)
- Third level: NOR of second-level outputs → XNOR

Why not others:
- (a) — produces XOR, not XNOR
- (b) — too few gates, does not produce XNOR
- (c) — too few gates, does not produce XNOR

Key rule: NOR is a universal gate. To quickly verify, substitute A=0, B=0 — XNOR must output 1. Eliminate any circuit that gives 0.

AI-generated — may contain errors