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Boolean logic — Lesson 2: Logic circuits and truth tables

Real digital systems combine several gates into a logic circuit. This lesson shows how to trace a circuit, build a truth table for it, and write the Boolean expression it represents — the three ways the same logic can be described.

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From gates to circuits

A B C AND OR output = (A . B) + C
  • A logic circuit connects two or more gates so the output of one gate becomes an input to another.
  • Work through it left to right: find each gate's output in turn until you reach the final gate.
  • The circuit as a whole takes the original inputs and produces one final output.
  • The same logic can be shown three ways: a circuit diagram, a Boolean expression, and a truth table.

Check you've got it

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1. How many rows are needed in the truth table for a logic circuit with 3 inputs?

2. In Boolean notation, how is 'A OR B' usually written?

3. A circuit computes (A AND B) OR C. If A = 1, B = 0 and C = 1, what is the output?

4. An OR gate's output is fed into a NOT gate. Which single gate gives the same overall result?

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