Characterizing NAND behavior: Which statement best describes a NAND gate's input–output relationship for the case of LOW inputs?

Introduction / Context:
NAND is a universal logic gate. Understanding its behavior for edge cases (all inputs LOW vs. all inputs HIGH) helps quickly predict outcomes and design with minimal gates. Here, the focus is on the output when inputs are LOW.

Given Data / Assumptions:

• Two-input NAND gate for simplicity (the conclusion generalizes).
• Logic levels: LOW = 0, HIGH = 1.

Concept / Approach:
NAND is the inversion of AND. The AND of two LOWs is 0, and then inverting yields 1. Therefore, with (0, 0) applied to a NAND, the output is HIGH. In general, NAND gives LOW only when all inputs are HIGH; for any other combination (including all LOW), it outputs HIGH.

Step-by-Step Solution:

Verification / Alternative check:
Quick truth table check: (0,0)→1; (0,1)→1; (1,0)→1; (1,1)→0. Only the all-HIGH case creates a LOW output, consistent with the rule of NAND.

Why Other Options Are Wrong:

• LOW inputs and a LOW output: That is the AND behavior, not NAND.
• HIGH inputs and a HIGH output: NAND of (1,1) is 0, not 1.
• None of these: One option is correct as shown.

Common Pitfalls:
Mixing AND and NAND logic; forgetting that NAND inverts the AND result. Also watch ambiguous phrasing—always compute with simple cases to confirm intuition.

Final Answer:
LOW inputs and a HIGH output