Boolean logic: OR

The idea

OR is a Boolean operator that combines two inputs so the output is 1 when at least one input is 1, and 0 only when both inputs are 0. For inputs A and B the four rows are 0,0; 0,1; 1,0; 1,1, and the OR column reads 0, 1, 1, 1. The rule extends to three or more inputs: the output is 1 if any input is 1, and 0 only if every input is 0. In logic circuits OR is drawn as a curved-input shield-shaped gate, and in expressions it may appear as a plus sign or as the word OR. A quick check is to ask whether any input is 1: if so, the OR output must be 1. Distinguishing OR from AND and from XOR is essential before analysing combined circuits.

What earns the marks

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

Common mistakes and how to put them right

• Confusing OR with AND: the learner requires both inputs to be 1 for an output of 1. Correction: OR needs only one input to be 1.

• Treating OR as exclusive, so that 1,1 gives 0.

  Put it right: Inclusive OR gives 1 when both inputs are 1 as well as when one is.

• Reading the plus notation or the shield-shaped symbol as AND. Correction: the plus sign and the shield shape both denote OR.

Exam tips

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