Topic 10 · Boolean Logic · 10.3

The AND Logic Gate

The AND gate produces an output of 1 only when both of its inputs are 1.

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Invitation

What must you have before you can go?

Imagine your teacher says:

“You can only go on the school trip if you have your permission slip AND your payment.”

Having only one is not enough. You need both.

That is the behaviour of an AND gate: both conditions must be true.
School trip rule
Permission slip ✓
Payment ✓
↓ AND
Go on the trip 🚌
Big Idea

The AND gate checks two inputs

An AND gate has two inputs and one output.

The output is 1 only when input A and input B are both 1.

A = 1Permission slip
+
B = 1Payment
→
X = 1Go on trip
Both inputs are 1, so the output is 1.
Visual Guide

The AND gate symbol

Two input lines enter the left side of the gate. One output line leaves the right side.

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

Read the gate from left to right: inputs → rule → output.
AND gate
ABX
Bridge

Only one combination unlocks the output

Slip ✗ + Payment ✗
Stay at school
Slip ✓ + Payment ✗
Stay at school
Slip ✗ + Payment ✓
Stay at school
Slip ✓ + Payment ✓
Go on the trip
The AND gate outputs 1 only in the final combination.
Truth Table

Every possible input combination

A truth table shows every possible pair of inputs and the output produced.

ABX
000
010
100
111
Find the row where both inputs are 1. That is the only row where X is 1.
Logic Expression

Writing the AND rule

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

X = A AND B

This means X is 1 only when A and B are both 1.

Read it aloud as: “X equals A AND B.”
Worked Example

Find the output

Question

An AND gate receives A = 1 and B = 0. What is the output X?

“X = 0 because both inputs are not 1.”
Exam Explainer

Three facts worth remembering

Two InputsAn AND gate compares A and B.
Both RequiredA and B must both be 1.
One OutputThe gate produces X.
Exam answer: “An AND gate outputs 1 only when both inputs are 1.”
Common Mistake

One input of 1 is not enough

✗ Incorrect

A = 1 and B = 0 gives X = 1.

✓ Correct

A = 1 and B = 0 gives X = 0.

Remember: AND means both—not either one.
Summary

AND means both

InputsTwo binary inputs.
RuleBoth must be 1.
OutputOne binary result.
Final rule: X = 1 only when A = 1 and B = 1.