Mission 1 · Spec 2.4.1
Logic gates and truth tables
The AND, OR and NOT gates, their symbols, and the truth tables that describe them.
- Starter 5 min
- Learn 10 min
- Lab 15 min
- Quiz 10 min
- Exam 10 min
Two keys to launch
A rocket launches only if both commanders turn their keys. A fire alarm sounds if either detector goes off. Describe each rule in one word.
Reveal
Rocket: AND. Alarm: OR. These rules are built as logic gates, the basic components of every processor.
Key ideas
| Gate | Output is 1 (True) when… | Notation |
|---|---|---|
| AND | both inputs are 1 | A ∧ B |
| OR | at least one input is 1 | A ∨ B |
| NOT | the input is 0 | ¬A |
A truth table shows every combination of inputs: 4 rows for 2 inputs, 8 rows for 3 inputs. OCR also accepts the words AND, OR and NOT.
Gate playground
Exam-style questions
1. Complete the truth table for an OR gate.
[2 marks]Mark scheme
- Outputs 0, 1, 1, 1 for inputs 00, 01, 10, 11 (2); 1 mark for three correct
2. Draw the logic gate symbol for NOT and state its output when the input is 1.
[2 marks]Mark scheme
- Triangle with a small circle at the output (1)
- Output is 0 (1)
TUTOR NOTES
- Misconception: OR is "one or the other but not both".
- Exam habit: list inputs in binary counting order: 00, 01, 10, 11.
Mission 2 · Spec 2.4.1
Combining gates
Logic diagrams with up to three inputs, Boolean expressions, and completing their truth tables.
- Starter 5 min
- Learn 10 min
- Lab 20 min
- Quiz 10 min
- Exam 10 min
The heater
A heater should come on when it's cold and the window is not open. How would you connect gates for that rule?
Reveal
Pass the window sensor through a NOT gate, then feed it and the cold sensor into an AND gate: Heater = Cold ∧ ¬Window.
Key ideas
- Work through a circuit from left to right, one gate at a time.
- Add columns to your truth table for intermediate results (e.g. A ∧ B), then work out the final output.
- Brackets in an expression show which part is worked out first: (A ∧ B) ∨ ¬C.
Circuit builder
Complete the truth table for each circuit, then try a new one.Exam-style questions
1. Write the Boolean expression for a circuit where A and B enter an OR gate, and its output enters an AND gate with C.
[2 marks]Mark scheme
- (A ∨ B) (1)
- ∧ C, giving Q = (A ∨ B) ∧ C (1); accept (A OR B) AND C
2. Complete the truth table for Q = ¬(A ∧ B).
[2 marks]Mark scheme
- Outputs 1, 1, 1, 0 for inputs 00, 01, 10, 11 (2); 1 mark for three correct
TUTOR NOTES
- Exam habit: intermediate columns earn marks and prevent slips.
- Extension: build XOR from AND, OR and NOT.