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

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:

  • 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

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