For example the expression (A AND B) OR (NOT C) would be represented as:

The idea

This statement introduces a worked example of translating a worded Boolean expression into symbols. The expression combines A AND B inside brackets, then ORs that result with the NOT of C. Using the agreed notation, AND becomes a dot between A and B, OR becomes a plus sign, and NOT C becomes C with an overbar. The brackets are kept because they show that A AND B is evaluated as one group before the OR is applied. So the symbolic form places a dot between A and B inside brackets, then a plus sign, then C carrying an overbar. When answering, translate each gate in turn, keep the brackets in the same position and check that every input appears once with the correct symbol.

What earns the marks

• AND is represented by a dot placed between A and B.
• The group A AND B is enclosed in brackets to preserve evaluation order.
• OR is represented by a plus sign joining the bracketed group to the NOT term.
• NOT C is represented by C with an overbar above it.
• The complete symbolic expression keeps the brackets and uses each correct symbol once.

Common mistakes and how to put them right

• Dropping the brackets so the OR appears to apply only to B.

  Put it right: Keep the brackets around A AND B.

• Writing NOT C as a minus sign before C.

  Put it right: Place an overbar above C.

• Using a plain plus for the AND group.

  Put it right: The dot represents AND and the plus represents OR.

• Reversing the order of the two groups.

  Put it right: Keep the bracketed AND group first, then the OR, then the NOT term.

Exam tips

• Translate one gate at a time, starting with the innermost brackets.
• Keep brackets exactly where the wording places them before simplifying.
• Re-read the finished expression and name each symbol to confirm it matches the original wording.