Combinational logic identification: What function results when an inverter is added to the output of an AND gate?

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:

• Base function: AND.
• Modification: add an inverter after the AND output.
• All logic signals are binary.

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