Topic 10 · Boolean Logic · 10.2

The NOT Logic Gate

The NOT gate has one simple job: it reverses the input and produces the opposite binary value.

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Invitation

What if the output always did the opposite?

Imagine a switch that works backwards.

When the input is ON, the output becomes OFF. When the input is OFF, the output becomes ON.

That is the entire behaviour of a NOT gate: it always gives the opposite answer.
Opposite behaviour
1 → 0ON becomes OFF
0 → 1OFF becomes ON
Big Idea

The NOT gate reverses one input

A NOT gate has only one input and one output.

The small circle on the gate symbol shows that the signal is inverted.

A = 1Input
→
X = 0Output
One input enters. The opposite value leaves.
Bridge

Think of an automatic night light

A light sensor can detect whether it is bright outside.

If the sensor input is 1 because daylight is present, the NOT gate produces 0 and the lamp stays off.

If the sensor input is 0 because it is dark, the NOT gate produces 1 and the lamp switches on.

The lamp does the opposite of the daylight sensor.
Night-light behaviour
Bright outside = 1
↓ NOT
Lamp off = 0
Dark outside = 0
↓ NOT
Lamp on = 1
Truth Table

Every possible input and output

A truth table shows every possible input and the output produced by the gate.

AX
01
10
There are only two rows because a NOT gate has one input with two possible values.
Logic Expression

Writing the NOT rule

The input is labelled A and the output is labelled X.

X = NOT A

This means: X contains the opposite Boolean value to A.

Read it aloud as: “X equals NOT A.”
Worked Example

Find the missing output

Question

A NOT gate receives the input A = 0. What is the output X?

“X = 1 because a NOT gate produces the opposite of the input.”
Exam Explainer

Three facts worth remembering

One InputA NOT gate never has two inputs.
Opposite Output0 becomes 1 and 1 becomes 0.
Small CircleShows that the signal is inverted.
Exam answer: “A NOT gate reverses its single input to produce the opposite output.”
Common Mistake

Do not copy the input into the output

✗ Incorrect

Input 1 produces output 1.

✓ Correct

Input 1 produces output 0.

Remember: NOT means reverse, invert or opposite.
Summary

NOT means opposite

InputOnly one binary input.
RuleReverse the value.
OutputOne opposite binary value.
Final rule: If A is 0, X is 1. If A is 1, X is 0.