NAND gate behavior check: For a NAND gate (AND followed by inversion), all inputs must be _____ to produce a LOW (0) output.

Introduction / Context:
NAND is one of the universal logic gates. Understanding its truth behavior is essential because NAND gates can implement any combinational logic. Since a NAND is an AND followed by an inverter, it produces the complement of an AND output.

Given Data / Assumptions:

• NAND = NOT(AND(inputs)).
• We are interested in the condition that yields a LOW (0) at the output.
• Input signals are standard binary logic levels (0 for LOW, 1 for HIGH).

Concept / Approach:
An AND gate produces 1 only when all inputs are 1 (HIGH). The NAND inverts that: output is 0 only when the AND would be 1, i.e., when all inputs are HIGH. In every other case (at least one input LOW), AND yields 0 and NAND yields 1.

Step-by-Step Solution:
Recognize AND truth: all HIGH → 1; otherwise → 0.Apply inversion: NAND output = NOT(AND output).Therefore, NAND output is LOW only when all inputs are HIGH.

Verification / Alternative check:
Create a simple two-input truth table; extend to N inputs. For inputs (1,1), AND=1 → NAND=0. For any input set containing a 0, AND=0 → NAND=1. The logic holds for any number of inputs.

Why Other Options Are Wrong:
“low” or “0's” would make AND=0, thus NAND=1 (HIGH). “some low and some high” also makes AND=0, so NAND=1. “None of the above” is wrong because “high” is correct.

Common Pitfalls:
Confusing AND and OR behavior; forgetting that NAND is the exact complement of AND.

Final Answer:
high