Number Base Converter — Binary, Octal, Decimal and Hexadecimal Converter
Our free number base converter instantly converts between binary (base 2), octal (base 8), decimal (base 10) and hexadecimal (base 16). Type in any field and all others update in real time. Essential for computer science students, programmers, network engineers and anyone working with low-level systems, bitwise operations, colour codes or memory addressing.
Why Do Computers Use Different Number Bases?
Computers only understand binary (base 2) — the physical on/off states of transistors. Humans, however, find binary hard to read. Hexadecimal (base 16) was adopted as a convenient shorthand because one hex digit represents exactly four binary digits (a nibble), making it easy to represent memory addresses, colour codes and byte values. Octal (base 8) was historically used in older Unix systems for file permissions.
Number Base Reference Guide
- Binary (base 2) — digits 0–1. Used internally by all digital computers. Each digit is one bit.
- Octal (base 8) — digits 0–7. Used in Unix file permissions (e.g. chmod 755 = rwxr-xr-x)
- Decimal (base 10) — digits 0–9. The human standard numbering system
- Hexadecimal (base 16) — digits 0–9 and A–F. Used for memory addresses, HTML/CSS colours, MAC addresses, SHA hashes, IPv6 addresses
Common Conversions
- 255 decimal = FF hex = 11111111 binary (maximum value of one byte)
- 0 decimal = 00 hex = 00000000 binary
- 16 decimal = 10 hex = 10000 binary
- #FF5733 (orange colour) = R:255 G:87 B:51 in decimal
- chmod 755 = 111 101 101 binary = rwxr-xr-x
Hexadecimal in Networking
Hex is used throughout networking: MAC addresses are 6 bytes written in hex (e.g. 00:1A:2B:3C:4D:5E), IPv6 addresses are 128 bits written as 8 groups of 4 hex digits, and subnet masks are sometimes expressed in hex for router configurations.