Logic gates
- AND: the output is 1 only if both inputs are 1.
- OR: the output is 1 if at least one input is 1.
- NOT: the output is the opposite of the input.
- (AQA) XOR: the output is 1 if the two inputs are different.
Truth tables
- A truth table shows the output for every combination of inputs. 2 inputs give 4 rows; 3 inputs give 8 rows (2ⁿ rows for n inputs).
- AND: 0 0 → 0, 0 1 → 0, 1 0 → 0, 1 1 → 1. OR: 0 0 → 0, 0 1 → 1, 1 0 → 1, 1 1 → 1. NOT: 0 → 1, 1 → 0.
Logic circuits and expressions
- Gates can be joined into circuits. P = NOT (A AND B) is 0 only when A and B are both 1.
- Work through a circuit one gate at a time, adding a column to the truth table for each gate's output.
- Expressions may use symbols. OCR writes AND as ∧, OR as ∨ and NOT as ¬. AQA writes A AND B as A·B, A OR B as A + B, and NOT A as A with a bar over it.
Using logic
- Logic is used in program conditions and in real systems. An alarm might sound if (a door is open OR a window is open) AND the alarm is set.
Key terms
- Logic gate
- An electronic component that carries out a Boolean operation on its inputs.
- AND gate
- Outputs 1 only when both inputs are 1.
- OR gate
- Outputs 1 when at least one input is 1.
- NOT gate
- Outputs the opposite of its single input.
- XOR gate
- Outputs 1 when the two inputs are different.
- Truth table
- A table showing the output for every possible combination of inputs.
- Boolean expression
- A statement using AND, OR and NOT that is either true or false.