Exclusive-NOR (XNOR) truth: is the output HIGH when inputs are unequal?

Introduction / Context:
Exclusive-NOR (XNOR) is a fundamental logic gate widely used in equality detectors, comparators, and parity checking. This item tests the core truth condition for XNOR versus XOR.

Given Data / Assumptions:

• Standard two-input XNOR gate.
• Logic levels use conventional binary 0 and 1.
• No timing hazards or analog details; we rely on ideal Boolean behavior.

Concept / Approach:
XOR is HIGH when inputs are different (unequal). XNOR is the complement of XOR, so it is HIGH when inputs are the same (equal). Therefore, the claim that XNOR is HIGH for unequal inputs contradicts its definition.

Step-by-Step Solution:

Verification / Alternative check:
Build the truth table: 00 → 1, 01 → 0, 10 → 0, 11 → 1 for XNOR. Unequal pairs (01,10) give 0. Equal pairs (00,11) give 1. This independently confirms the reasoning.

Why Other Options Are Wrong:
“Correct” would describe XOR, not XNOR. “Only when both inputs are LOW” is incomplete; XNOR is also HIGH when both are HIGH. “Only when both inputs are HIGH” similarly misses the 00 case. “Only with open-collector outputs” confuses output structure with logic function; collector configuration does not change truth conditions.

Common Pitfalls:
Learners often swap XOR and XNOR semantics or forget that XNOR is an equality detector. Another pitfall is thinking output stage hardware affects the Boolean function—it does not for ideal logic definitions.

Final Answer:
Incorrect