Exclusive-NOR as an equality detector Why is an exclusive-NOR (XNOR) gate also referred to as an equality gate?

Introduction / Context:In digital logic, comparators detect when two signals match. The exclusive-NOR (XNOR) gate implements the simplest 1-bit equality function, making it a building block for multi-bit equality comparators.

Given Data / Assumptions:

• XNOR truth table yields 1 when inputs are the same (00 or 11).
• Opposite inputs (01 or 10) produce 0.
• Inputs are single-bit logical values.

Concept / Approach:Equality means A equals B. The Boolean function for equality is X = A XNOR B. This can also be written as X = (A AND B) OR (NOT A AND NOT B).

Step-by-Step Solution:

Verification / Alternative check:Algebraic form X = A*B + A'*B' matches the equality condition because each product term covers one of the equal-input cases.

Why Other Options Are Wrong:

• The output is false if the inputs are equal: This describes XOR, not XNOR.
• The output is true if the inputs are opposite: Also describes XOR, not XNOR.

Common Pitfalls:Confusing XOR and XNOR symbols or names, and forgetting that the bar (or bubble) on XOR indicates inversion of the XOR result.

Final Answer:The output is true if the inputs are equal.