Topic 10 · Boolean Logic · 10.10

Representing Logic Expressions

Learn how to turn a logic circuit into a logic expression by following the signal from the inputs to the output.

Start the lesson
Invitation

Can you read a circuit like a sentence?

Imagine following a road from your house to school. You simply follow the route from start to finish.

Logic circuits are read the same way. Follow the signal from the inputs to the output.

A circuit is a picture. A logic expression is the written version of the same rule.
Read left to right
Inputs
→
Gate
→
Output
Big Idea

Every circuit can be written

Identify the input labels, identify the gate, then write the output.

X = A AND B
Nothing changes except the way the information is represented.
Visual Guide

Turn the circuit into a sentence

Read every logic circuit in the same order:

1Find the input labels.
2Identify the logic gate.
3Write the output.
Always follow the signal from left to right.
Circuit → Expression
A B X
X = A AND B
Worked Example

Point to each part

Read the diagram
Inputs → A and B
↓
Gate → AND
↓
Output → X

Question

A and B are connected to an AND gate. The output is X.

“X = A AND B”
The picture and the expression describe exactly the same behaviour.
Hinge Question

Which part tells you the operator?

Question

When converting a circuit into a logic expression, which part tells you whether to write AND, OR, XOR or NAND?

“The logic gate symbol tells you which operator to use.”
Exam Explainer

Use the same method every time

InputsCopy labels exactly.
GateIdentify behaviour.
OutputWrite output = expression.
Exam tip: Follow the signal from left to right.
Common Mistake

Always copy the labels from the circuit

The circuit uses P, Q and R
P Q R
Copy P → first input
Copy Q → second input
Copy R → output

✗ Incorrect

X = A AND B

The circuit never used A, B or X.

✓ Correct

R = P AND Q

Use the labels shown in the circuit.

Remember: The logic stays the same. Only the labels change. Always copy the labels given in the question.
Summary

Pictures and expressions say the same thing

FindInputs.
NameThe gate.
WriteThe expression.
Final rule: A logic expression is simply the written version of a logic circuit.