Difficulty: Easy
Correct Answer: NAND
Explanation:
Introduction / Context:
Constructing logic from primitive gates is a common exercise. Many complex functions can be reduced to combinations of AND, OR, and NOT (inverter) operations. Recognizing these composites quickly is useful in design and troubleshooting.
Given Data / Assumptions:
Concept / Approach:
By definition, NAND is the complement of AND. That is, NAND(A,B,...) = NOT(AND(A,B,...)). Therefore, if you take an AND gate and simply invert its output, the resulting function is NAND. This identity generalizes to any number of inputs.
Step-by-Step Solution:
Start with Y = AND(inputs).Apply inversion: Z = NOT(Y).Thus Z = NOT(AND(inputs)) = NAND(inputs).
Verification / Alternative check:
Truth tables validate that the output is LOW only when all inputs are HIGH—exactly the behavior of a NAND gate.
Why Other Options Are Wrong:
NOR = NOT(OR), not NOT(AND). XOR is exclusive OR and cannot be formed by a single inversion of AND. OR is the original OR function, not the complement of AND.
Common Pitfalls:
Confusing De Morgan’s laws; remember that NOT(AND) is NAND and NOT(OR) is NOR.
Final Answer:
NAND
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