What Is Binary?

Binary (base-2) is the number system used internally by all modern computers. It uses only two digits: 0 and 1, corresponding to the two states of an electronic switch (off/on, low voltage/high voltage).

Every number, character, image, and instruction processed by a CPU is ultimately represented as a sequence of bits (binary digits).

The Four Common Number Bases

Base	Name	Digits	Common use
2	Binary	0–1	CPU, memory, data storage
8	Octal	0–7	Unix file permissions (chmod 755)
10	Decimal	0–9	Everyday counting
16	Hexadecimal (hex)	0–9, A–F	Memory addresses, colours, hash values

How Positional Notation Works

Each position in a number represents a power of the base:

Decimal 2026:

2 × 10³ + 0 × 10² + 2 × 10¹ + 6 × 10⁰
= 2000 + 0 + 20 + 6 = 2026

Binary 11111101010 (= 2026 in decimal):

1×2¹⁰ + 1×2⁹ + 1×2⁸ + 1×2⁷ + 1×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 1024 + 512 + 256 + 128 + 64 + 32 + 0 + 8 + 0 + 2 + 0 = 2026

Converting Decimal to Binary

Divide by 2 repeatedly, recording the remainder:

2026 ÷ 2 = 1013 r 0
1013 ÷ 2 = 506  r 1
506  ÷ 2 = 253  r 0
253  ÷ 2 = 126  r 1
126  ÷ 2 = 63   r 0
63   ÷ 2 = 31   r 1
31   ÷ 2 = 15   r 1
15   ÷ 2 = 7    r 1
7    ÷ 2 = 3    r 1
3    ÷ 2 = 1    r 1
1    ÷ 2 = 0    r 1

Read remainders from bottom to top: 11111101010

Hexadecimal — Compact Binary Representation

Each hex digit represents exactly 4 bits (a "nibble"), making it a convenient shorthand:

Hex	Binary	Decimal
0	0000	0
5	0101	5
A	1010	10
F	1111	15

Example: Hex #FF5733 (an orange-red colour):

FF = 1111 1111 = 255 (red channel)
57 = 0101 0111 = 87  (green channel)
33 = 0011 0011 = 51  (blue channel)

Octal and Unix Permissions

Unix file permissions are often shown in octal. Each digit represents three bits (read, write, execute):

chmod 755 → 7=111 (rwx), 5=101 (r-x), 5=101 (r-x)
Owner: read+write+execute
Group: read+execute
Others: read+execute

Bits, Bytes, and Beyond

Unit	Bits
1 bit	1
1 nibble	4
1 byte	8
1 kilobyte (KB)	8,192
1 megabyte (MB)	8,388,608

Computers process data in multiples of 8 bits because 8 bits (one byte) can represent 256 values (0–255), which conveniently covers the ASCII character set, a colour channel value, and many protocol fields.

Use the Number Base Converter to convert any number between binary, octal, decimal, and hexadecimal.