Equality detection: Which gate provides a HIGH output exactly when its two inputs have equal logic levels (both 0 or both 1)?

Introduction / Context:Comparing two binary signals is a common task. The equality function outputs HIGH when inputs match. Recognizing which primitive gate directly implements equality simplifies design work for comparators and parity logic.

Given Data / Assumptions:

• Two-input standard logic gates under positive logic.
• Goal is equality detection (A = B).

Concept / Approach:By definition, XOR is HIGH when inputs differ; therefore its complement, XNOR, is HIGH when inputs are equal. The XNOR truth table places 1s at (0,0) and (1,1) and 0s at (0,1) and (1,0).

Step-by-Step Solution:

Verification / Alternative check:Build a small truth table or evaluate A′B′ + AB for all four input pairs; outputs are 1 only on equality rows, confirming XNOR.

Why Other Options Are Wrong:

• XOR: Detects inequality.
• NAND/NOR/AND: Do not implement equality; their truth tables do not match equality-only HIGH behavior.

Common Pitfalls:Confusing XOR with XNOR; attempting to build equality with AND/OR and inverters when a single XNOR suffices.

Final Answer:XNOR gate