Exclusive-NOR (XNOR) gate behavior In digital electronics, the exclusive-NOR gate outputs logic 1 when both inputs have the same logic level. For a 2-input XNOR gate, which input combination will produce an output of 1?

Introduction / Context:
Exclusive-NOR (XNOR) is a fundamental digital logic gate used for equality detection. It outputs logic 1 when both inputs are equal (both 0 or both 1) and outputs logic 0 when the inputs differ. Understanding this truth relationship is essential for comparators, parity checkers, and error-detection circuits.

Given Data / Assumptions:

• Gate: 2-input XNOR.
• We test listed input pairs to determine which yields output 1.
• Logic levels: 1 = HIGH, 0 = LOW.

Concept / Approach:
The XNOR operation implements logical equality. For inputs A and B, XNOR can be expressed as A XNOR B = (A AND B) OR (A' AND B'). Equivalently, it is the complement of XOR: A XNOR B = (A XOR B)'. Thus, output is 1 when A = B and 0 otherwise.

Step-by-Step Solution:

Verification / Alternative check:
Construct the full truth table: equal pairs (0,0) and (1,1) produce 1; unequal pairs produce 0. Since 1,1 is not listed, 0,0 is the only valid choice here.

Why Other Options Are Wrong:

• A = 1, B = 0: unequal inputs yield 0, not 1.
• A = 0, B = 1: unequal inputs yield 0, not 1.
• none of the above: incorrect because 0,0 is valid.

Common Pitfalls:
Confusing XOR with XNOR; assuming XNOR is 1 only when both inputs are 1 (that is AND), or overlooking that 0,0 also satisfies equality and therefore produces 1 for XNOR.

Final Answer:
A = 0, B = 0