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AQA GCSE · Question 03.4 · Computer systems
A green light (G) in the game switches on if all of the following conditions are true:
- sensor D is off
- sensor L is off
- sensor W is on.
Write a Boolean expression for this logic circuit. You must use Boolean expression operators in your answer.
A green light (G) in the game switches on if all of the following conditions are true:
- sensor D is off
- sensor L is off
- sensor W is on.
Write a Boolean expression for this logic circuit. You must use Boolean expression operators in your answer.
How to approach this question
1. Translate each condition into a Boolean term:
- "sensor D is off" becomes `NOT D`.
- "sensor L is off" becomes `NOT L`.
- "sensor W is on" becomes `W`.
2. The condition "all ... are true" means these terms must be connected by the AND operator.
3. Combine the terms: `(NOT D) AND (NOT L) AND W`.
4. The final expression is `G = (NOT D) AND (NOT L) AND W`.
5. You can also use other standard notations, such as a bar over the letter for NOT and a dot for AND: `G = D̅ . L̅ . W`.
Full Answer
G = (NOT D) AND (NOT L) AND W
or using alternative notation:
G = D̅ . L̅ . W
A Boolean expression uses variables and operators to represent a logic circuit.
- **Variables:** The sensors D, L, and W.
- **Conditions:**
- "sensor D is off" is represented as `NOT D`.
- "sensor L is off" is represented as `NOT L`.
- "sensor W is on" is represented as `W`.
- **Operator:** The phrase "if all of the following conditions are true" implies the `AND` operator, which connects all the conditions.
Combining these gives the expression: `(NOT D) AND (NOT L) AND W`.
This is assigned to the output G, so the full expression is `G = (NOT D) AND (NOT L) AND W`.
Alternative notations are also correct, for example, using a bar for NOT and a dot for AND: `G = D̅ . L̅ . W`.
Common mistakes
✗ Using OR instead of AND.
✗ Forgetting to apply NOT to D and L.
✗ Applying NOT to W incorrectly.
✗ Using incorrect notation for the operators (e.g., using programming language symbols like `!` or `&&` unless specified as acceptable).
Practice the full AQA GCSE Computer Science Paper 2
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