Identify the gate by its behavior: “Output is OFF (0) when inputs are the same, and ON (1) when inputs are different.” Which standard gate matches this description?

Introduction / Context:Recognizing a logic function from a verbal description is a core digital skill. The statement describes a detector that turns ON only when inputs differ. This behavior underpins parity generation, error checking, and bit-wise comparison operations in CPUs and communication systems.

Given Data / Assumptions:

• Two-input gate, positive logic.
• “ON” maps to logic 1, “OFF” maps to logic 0.
• Inputs are binary values A and B.

Concept / Approach:The exclusive-OR (XOR) gate outputs 1 only when exactly one input is 1; equivalently, when inputs differ. Its complement, XNOR, outputs 1 when inputs are equal. AND/NOR/Buffer do not show this “difference detection” behavior. Therefore, the verbal rule exactly matches XOR.

Step-by-Step Solution:

Verification / Alternative check:Algebraic form: XOR(A,B) = A′B + AB′. This is true when exactly one term is true, i.e., inputs differ. Hardware libraries list XOR as a “difference” or “parity” gate, confirming the match.

Why Other Options Are Wrong:

• Exclusive-NOR (XNOR): Outputs 1 when inputs are the same, opposite of the description.
• AND: Requires both inputs 1; ignores equality/inequality cases.
• NOR: Outputs 1 only for 00; not a difference detector.
• Buffer: Copies a single input; does not combine two inputs.

Common Pitfalls:Confusing XOR and XNOR due to similar naming; forgetting that XOR highlights differences while XNOR highlights equality.

Final Answer:Exclusive-OR (XOR)