NOR gate truth-table understanding without a figure For a 2-input NOR gate, choose the correct statement describing its truth table and output behavior for all input combinations.

Introduction / Context:
NOR is a fundamental universal gate widely used in logic synthesis. Recognizing its truth-table behavior by description saves time when reading or repairing circuits without printed tables or figures.

Given Data / Assumptions:

• Two inputs: A and B, each 0 or 1.
• NOR output is the complement of OR: Y = (A + B)̄.

Concept / Approach:
Compute the OR first; then invert it. OR is 1 if at least one input is 1; otherwise 0. Therefore, NOR is 1 only in the single case when OR is 0, namely when both inputs are 0.

Step-by-Step Solution:
Case A=0, B=0: OR=0 → NOR=1.Case A=0, B=1: OR=1 → NOR=0.Case A=1, B=0: OR=1 → NOR=0.Case A=1, B=1: OR=1 → NOR=0.

Verification / Alternative check:
Truth-table reconstruction confirms that only the (0,0) input pair yields output 1. Karnaugh maps also show a single minterm at ĀB̄ for Y.

Why Other Options Are Wrong:
The statement that output is 1 whenever any input is 1 describes OR, not NOR. Saying output is 0 only when both inputs are 0 flips the correct case. Output toggling independently of inputs has no basis in deterministic combinational logic.

Common Pitfalls:
Confusing NOR with NAND (which is 0 only when both inputs are 1) or with OR. Omitting the inversion step after computing OR.

Final Answer:
Output is 1 only when both inputs are 0