Boolean logic: AND

The idea

AND is a Boolean operator that combines two inputs so the output is 1 only when both inputs are 1; in every other case the output is 0. Learners should be able to complete a two-input truth table: with inputs A and B, the four rows are 0,0; 0,1; 1,0; 1,1, and the AND column reads 0, 0, 0, 1. The same rule extends to three or more inputs, where the output is 1 only if every input is 1. In logic circuits AND is drawn as a D-shaped gate, and in written expressions it may appear as a dot or as the word AND. A useful check is to ask whether any input is 0: if so, the AND output must be 0. Recognising this operator correctly is essential before combining gates in larger circuits.

What earns the marks

• States that AND outputs 1 only when all its inputs are 1.
• States that AND outputs 0 when any input is 0.
• Correctly completes a two-input AND truth table as 0, 0, 0, 1 for input pairs 00, 01, 10, 11.
• Applies AND correctly to three or more inputs, giving 1 only when every input is 1.
• Recognises the AND gate symbol or the word/dot notation for AND in an expression.

Common mistakes and how to put them right

• Confusing AND with OR: the learner treats AND as giving 1 when either input is 1. Correction: AND needs every input to be 1; OR needs only one.

• Assuming AND always outputs 1 for the input pair 1,1 regardless of other inputs in a multi-input gate.

  Put it right: Check all inputs, not just two.

• Reading the dot notation or the D-shaped symbol as OR. Correction: the dot and the D-shape both denote AND.

Exam tips

• Write out the full truth table row by row and check each row against the rule that any 0 input forces a 0 output.
• When a question shows a circuit, label each gate with its operator before working out intermediate values.
• Use the phrase 'both inputs must be 1' as a quick self-check when answering multiple-choice options.