Number systems: binary, octal, decimal and hexadecimal

What is a number system?

A number system is a way of writing numbers using a specific set of symbols. We are used to the decimal (0–9), but others are also used in computer science.

Basic systems

Binary (radix 2)

Symbols: 0, 1. The basis of how computers work. Each bit is one binary digit.

Octal (base 8)

Characters: 0–7. Used on Unix systems for access rights (chmod 755).

Decimal (base 10)

Characters: 0–9. The everyday system we use.

Hexadecimal (base 16)

Symbols: 0–9, A–F. Used for CSS colors, memory addresses, MAC addresses.

Correspondence table

How to translate manually

From decimal to binary

Divide the number by 2, writing the remainder from bottom to top. For example: 13 → 1101.

From binary to decimal

Multiply each digit by 2 to the power of its position: 1101 = 8+4+0+1 = 13.

Use Numeral System Converter for instant conversion.

See also: Color converter, Data converter, Angle converter