Topic 10 · Boolean Logic · 10.11

Representing Problem Statements

Learn how to find the logic hidden inside everyday language and turn it into a gate, circuit and expression.

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Invitation

Can you spot the logic hidden in a sentence?

Read this problem statement:

“The alarm sounds if the front door OR the back door is opened.”

The sentence already tells you the behaviour. The word OR tells you which gate to use.

Problem statements often contain the logic gate in plain sight.
Words become logic
Front door
Back door
OR ↓
Alarm sounds
Big Idea

Find the behaviour words

Do not begin with the circuit. Begin with the words that describe the behaviour.

AND / bothBoth conditions are required.
OR / eitherOne or both conditions can be true.
NOTReverse the condition.
Exactly oneUse XOR.
Unless bothOften suggests NAND.
Only when neitherOften suggests NOR.
The nouns tell you what the inputs are. The behaviour words tell you which gate to use.
Visual Guide

Use the same translation path every time

Problem statement
→
Find behaviour words
→
Choose the gate
→
Write circuit or expression
Words → Behaviour → Gate → Representation.
Worked Example

Turn a sentence into logic

“The machine starts only if the safety guard is closed AND the start button is pressed.”
ASafety guard is closed.
BStart button is pressed.
GateAND — both conditions are required.
XMachine starts.
AND circuit
ABX
X = A AND B
More Examples

The behaviour is often already written for you

OR“The alarm sounds if the front door or back door opens.”
XOR“The light turns on when exactly one switch is active.”
NOT“The fan runs when the stop signal is not active.”
Read for behaviour before you draw anything.
Hinge Question

Which words reveal the gate?

Question

“The warning light turns on when exactly one of the two sensors is active.” Which gate should be used, and why?

“Use XOR because the phrase ‘exactly one’ means one input may be active, but not both.”
Exam Explainer

Use a reliable method

Step 1Underline the behaviour words.
Step 2Label the inputs and output.
Step 3Choose the gate and write the expression.
Exam tip: Do not rush to draw the circuit. First identify the behaviour.
Common Mistake

Do not focus only on the nouns

✗ Incorrect focus

Door, alarm, sensor, button.

These tell you what the system contains, but not how it behaves.

✓ Correct focus

AND, OR, NOT, both, either, exactly one.

These words reveal the logic.

Remember: Nouns identify the inputs. Behaviour words identify the gate.
Summary

Every problem statement contains a behaviour

ReadThe statement carefully.
RecogniseThe behaviour words.
RepresentThe behaviour using logic.
Final rule: Logic gates represent behaviours described in everyday language.