Combining Boolean Operators (AQA GCSE Computer Science)

Revision Note

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Combining Boolean Operators

  • Boolean operators can be combined to produce more complex expressions

  • The combination of two or more Boolean operators forms a logic expression

  • Brackets are used to clarify the order of operations

  • A logic diagram is a visual representation of combinations of Boolean operators within a logic circuit

  • An example would be Q = NOT(A OR B) // Q space equals open parentheses top enclose A plus B end enclose close parentheses

logic circuit1
  • In the diagram above, the inputs are represented by A and B

  • P is the output of the OR gate on the left and becomes the input of the NOT gate

  • Q is the final output of the logic circuit

  • This is a logic diagram for the Boolean expression Q = NOT(A OR B) // Q space equals space open parentheses top enclose A plus B end enclose close parentheses 

Examiner Tip

You may be asked to draw a logic circuit from a logic statement or a Boolean expression OR write the logical expression that is expressed in the logic diagram using Boolean expression operators

Logic circuits will be limited to a maximum of three inputs and one output

Example of combining Boolean operators

10-boolean-logic
  • P = (A OR B) AND NOT C // P space equals space open parentheses A plus B close parentheses space. space top enclose C

Worked Example

A green light (G) in a 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 [3]

Answer

  • D̅. L̅. W // (D̅. W). (L̅. W) 

Guidance

  • 2 marks if fully correct but using different notation, e.g. NOT D AND NOT L AND W

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