Equality detection in logic circuits: Which specialized gate outputs HIGH exactly when its two inputs are equal (both 0 or both 1)?

Introduction / Context:Equality comparators form a foundation for digital systems: address matching, error detection, and control logic often require checking whether two bits (or vectors) are the same. At the single-bit level, one standard gate directly realizes equality.

Given Data / Assumptions:

• Two binary inputs, A and B.
• We want output = 1 when A = B, and output = 0 when A ≠ B.
• Gate names use the “exclusive” family conventions.

Concept / Approach:Exclusive-OR (XOR) outputs 1 when inputs differ. Exclusive-NOR (XNOR), being the logical complement of XOR, outputs 1 when inputs are the same and 0 otherwise. Thus, XNOR serves as a 1-bit equality detector. For multi-bit equality, XNOR is applied bitwise and the results are ANDed together.

Step-by-Step Solution:

Verification / Alternative check:Construct a small truth table for A, B, and outputs of XOR/XNOR to confirm which aligns with equality.

Why Other Options Are Wrong:

Common Pitfalls:Confusing XOR with XNOR; forgetting that XNOR is the equality operator in many HDLs (often written as A = B for vectors, but implemented via XNOR chains).

Final Answer:exclusive-NOR