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) // $Q = (A + B)$

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) // $Q = (A + B)$

Exam 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 // $P = (A + B) . C$

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

Combining Boolean Operators (AQA GCSE Computer Science)

Revision Note