What Is the Binary Number System?

The binary number system is a number system that uses only two digits:

• 0

• 1

Computers use binary because electronic circuits have two states:

• ON

• OFF

These states can easily represent 1 and 0.

All data inside a computer — including numbers, text, images and sound — is stored in binary form.

computer ol

Why Computers Use Binary

Computers use binary because it is simple and reliable for electronic devices.

Electronic components such as transistors can easily represent:

Electrical StateBinary ValueOFF0ON1

This allows computers to process and store information efficiently.

Denary vs Binary

Humans normally use the denary (base-10) number system, which uses digits from 0 to 9.

Example:

Denary number
125

Binary number example
1010

Binary is called a base-2 system because it only uses two digits.

Converting Denary to Binary

Example: Convert 13 to binary

Divide repeatedly by 2.

DivisionRemainder13 ÷ 216 ÷ 203 ÷ 211 ÷ 21

Read the remainders from bottom to top:

13 = 1101

Converting Binary to Denary

Example: Convert 1011 to denary

Binary PositionValue1 × 880 × 401 × 221 × 11

Total:

8 + 2 + 1 = 11

So:

1011 (binary) = 11 (denary)

Why Binary Is Important in Computer Science

Understanding binary helps students learn:

• Data storage

• Computer processing

• Programming

• Logic circuits

Binary is one of the most important topics in Computer Science exams.

Exam Tip (2210 / 0478)

Students are often asked to:

• Convert denary to binary

• Convert binary to denary

• Perform binary addition

These questions appear frequently in Paper 1 exams.

Practice Question

Convert 25 to binary.

Answer

25 = 11001

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