Topic 10 · Boolean Logic · 10.6

The NOR Logic Gate

The NOR gate performs OR first, then reverses the answer.

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Invitation

What if the OR answer is reversed?

Imagine a school rule:

“The alarm stays off only when there is NO smoke OR heat.”

If either warning appears, OR gives 1 and NOR reverses it to 0. Only when both warnings are absent does the output become 1.

That is NOR behaviour: OR decides first, then NOT reverses the result.
Alarm rule
Smoke detected?
Heat detected?
OR ↓
Reverse the answer
Big Idea

NOR means NOT OR

A NOR gate has two inputs and one output.

It first checks whether either input is 1. It then reverses that result.

A = 0No smoke
OR
B = 0No heat
NOT →
X = 1Alarm clear
Both inputs are 0, so OR gives 0. NOR reverses this to 1.
Visual Guide

The NOR gate symbol

The NOR symbol looks like an OR gate with a small circle on its output.

The small circle means NOT. It reverses the OR result.

OR shape + output circle = NOR.
NOR gate
ABX
Bridge

Only one combination produces 1

0 + 0
Output 1
0 + 1
Output 0
1 + 0
Output 0
1 + 1
Output 0
A NOR gate outputs 1 only when both inputs are 0.
Truth Table

The opposite of OR

Compare the NOR outputs with the OR truth table. Every output is reversed.

ABX
001
010
100
110
Think OR first, then flip the output.
Logic Expression

Writing the NOR rule

The inputs are labelled A and B. The output is labelled X.

X = A NOR B

This means X is the opposite of A OR B.

Read it aloud as: “X equals A NOR B.”
Worked Example

Find the output

Question

A NOR gate receives A = 0 and B = 1. What is the output X?

“X = 0 because OR gives 1, then NOR reverses it to 0.”
Exam Explainer

Three facts worth remembering

Two InputsNOR compares A and B.
OR Then NOTThe OR result is reversed.
One OneOnly 0 OR 0 gives output 1.
Exam answer: “A NOR gate outputs 1 only when both inputs are 0.”
Common Mistake

Do not stop after OR

✗ Incorrect

A = 0 and B = 0 gives X = 0.

✓ Correct

OR gives 0, then NOR reverses it to X = 1.

Remember: The small output circle means reverse the answer.
Summary

NOR means OR, then opposite

Step 1Check A OR B.
Step 2Reverse the result.
Output1 only for 0, 0.
Final rule: NOR is the exact opposite of OR.