SYLLABUS 10.3 · PAPER 2 · ALSO FOR 0984 AND 2210

Logic circuits and logic expressions

This topic builds on the six logic gates. You need to move between three forms of the same logic: a circuit diagram, a logic expression and a truth table.

From a circuit to an expression

Start at the inputs and work towards the output, writing what each gate produces. A gate’s output becomes an input to the next gate, so wrap it in brackets. If A and B go into an AND gate, and its output goes into an OR gate with C, the expression is X = (A AND B) OR C.

From an expression to a circuit

Work from the innermost brackets outwards. Draw a gate for each bracketed part first, then feed their outputs into the gates that combine them. Label every input and the final output. Each gate must have the right number of inputs: one for NOT, two for the others in the syllabus.

Truth tables for circuits

Write every input combination (8 rows for three inputs), then add a working column for the output of each gate in the order the signals flow. The last column is the circuit’s output. Two circuits are equivalent if their output columns match on every row.

Where marks go

  • Leaving out brackets, so AND and OR are combined in a different order.
  • Drawing a gate with three inputs: the syllabus gates have at most two.
  • Not labelling the inputs and the output on a drawn circuit.
  • Skipping working columns and making a slip in the final output.
  • Writing NOT A AND B when NOT (A AND B) is meant; they give different results.

Try a question

2 MARKS · MARKED ON THIS PAGE

The logic circuit shown controls a warning light, X, on a school minibus dashboard. Write the logic expression for this circuit. Use brackets to show the order of the gates.

ABCX

Variables: A, B, C — use . or juxtaposition for AND, + for OR, and a trailing ' for NOT (e.g. A.C + B'C).

Fill in your answer first.