Boolean logic: XOR.

The idea

XOR (exclusive OR) is a two-input logic operation whose output is 1 only when the inputs differ. With inputs A and B, the output is 1 for A=0, B=1 and for A=1, B=0; it is 0 for A=0, B=0 and for A=1, B=1. A reliable method is to write the four input combinations in order (00, 01, 10, 11) and test each: count the number of 1s; XOR gives 1 when that count is exactly one, whereas OR gives 1 whenever at least one input is 1. So OR and XOR agree except for the 11 row, where OR gives 1 and XOR gives 0. The Boolean expression is A XOR B, sometimes written with the symbol ⊕. Recognise the gate's distinctive shape and be able to state its output for any given pair of inputs.

What earns the marks

• XOR outputs 1 only when exactly one input is 1 (the inputs differ).
• For inputs 0 and 0 the XOR output is 0.
• For inputs 0 and 1 the XOR output is 1.
• For inputs 1 and 0 the XOR output is 1.
• For inputs 1 and 1 the XOR output is 0, which distinguishes XOR from OR.
• XOR can be expressed as A XOR B (or A ⊕ B).

Common mistakes and how to put them right

• Confusing XOR with OR: the learner says 1 XOR 1 gives 1. Correction: XOR gives 0 when both inputs are 1 because the inputs do not differ.

• Treating XOR as AND: the learner says 0 XOR 1 gives 0. Correction: XOR gives 1 whenever exactly one input is 1, so 0 XOR 1 gives 1.

• Assuming XOR needs more than two inputs.

  Put it right: Apply the two-input rule to A and B directly.

• Reading the gate symbol wrongly.

  Put it right: The XOR symbol has an extra curved line before the OR shape.

Exam tips

• Write out the four input pairs 00, 01, 10, 11 and evaluate each before choosing an option.
• Use the test 'do the inputs differ?' to decide XOR output quickly.
• Check the 11 row specifically, since that is where XOR and OR differ.