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Boolean Logic and Logic Gates: Question 5

Syllabus 10.1, 10.2, 10.3

Multiple choice 1 mark

A student is simplifying a section of a circuit diagram and finds that this section always produces the same output as the logic expression NOT (A AND B), for every combination of inputs A and B.

Which single logic gate could replace this entire section of the circuit?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Step 1: Break down the expression

The expression is NOT (A AND B). This means: first combine A and B with an AND gate, then invert (NOT) that result.

Step 2: Recall which gate this defines

A gate whose output is the inverse of an AND gate’s output (that is, NOT (A AND B)) is by definition a NAND gate (“NOT AND”). Its output is 0 only when both inputs are 1, and 1 in every other case.

Step 3: Rule out the other options

  • AND on its own gives A AND B, not its inverse, so it does not match.
  • OR gives A OR B, which follows a completely different rule (1 whenever at least one input is 1) and is not equivalent to NOT (A AND B).
  • NOR is the inverse of OR (that is, NOT (A OR B)) which is a different expression from NOT (A AND B), even though both NAND and NOR are “inverted” gates.

Final answer

The single gate equivalent to NOT (A AND B) is NAND, option C.