Exclusive-NOR (XNOR) behavior For a standard 2-input exclusive-NOR gate, under which condition does the output go HIGH (logic 1)?

Introduction / Context:
Exclusive-NOR (XNOR) is the logical complement of XOR and is often used as an equality detector in digital comparators, address match circuits, and error-checking logic.

Given Data / Assumptions:

• 2-input XNOR with inputs A, B and output X.
• XNOR = NOT(XOR).
• Ideal logic levels 0 and 1.

Concept / Approach:
Since XOR outputs 1 when inputs differ, XNOR outputs 1 when inputs are the same. Common expression: X = A * B + NOT A * NOT B. This evaluates to 1 for (0,0) and (1,1) input pairs only.

Step-by-Step Solution:
Case A=0, B=0 → X = 0 * 0 + 1 * 1 = 1.Case A=0, B=1 → X = 0 * 1 + 1 * 0 = 0.Case A=1, B=0 → X = 1 * 0 + 0 * 1 = 0.Case A=1, B=1 → X = 1 * 1 + 0 * 0 = 1.

Verification / Alternative check:
Think of XNOR as “logical equality.” If A equals B, the output is HIGH; otherwise, LOW. Many digital comparators chain XNORs across bit-pairs and OR the inverted results to detect mismatches.

Why Other Options Are Wrong:

• “one HIGH, one LOW” describes XOR, not XNOR.
• “inputs are unequal” is XOR’s condition for HIGH, the opposite of XNOR.
• “none of the above” is false because “inputs are equal” is correct.

Common Pitfalls:

• Assuming XNOR is the same as OR or AND; it is a distinct equality operator.
• Forgetting that XNOR is the inverse of XOR and thus complements its truth table.

Final Answer:
the inputs are equal