Identify the equality gate Which logic gate outputs HIGH when both inputs are HIGH or both inputs are LOW (i.e., when the inputs are equal)?

Introduction / Context:
Digital systems frequently need to compare two signals. The gate that outputs HIGH when the inputs are the same implements equality at the 1-bit level and is commonly used in comparators and parity circuits.

Given Data / Assumptions:

• Two binary inputs A and B.
• We seek a gate that asserts when A equals B (00 or 11).

Concept / Approach:
The exclusive-NOR (XNOR) function is 1 exactly when inputs match. Boolean form: X = A*B + A'B'. This is the complement of XOR, which is 1 when inputs differ.

Step-by-Step Solution:

Verification / Alternative check:
Construct XNOR from simpler gates: two ANDs (AB and A'*B') feeding an OR implements equality, confirming the behavior.

Why Other Options Are Wrong:

• OR gate: Produces 0 only for 00; does not assert for 11 exclusively.
• Ex-OR gate: Asserts when inputs differ (01 or 10).
• NAND gate: Produces 0 only for 11; not an equality detector.

Common Pitfalls:
Confusing XOR with XNOR because of similar names; remember XNOR is the complemented XOR and corresponds to equality.

Final Answer:
Ex-NOR gate