What is a number base?
A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. The decimal system we use every day has base 10 — it uses the digits 0–9. Each position in a decimal number represents a power of 10. The number 425 means 4×100 + 2×10 + 5×1.
Other bases work the same way, just with different numbers of digits and different powers. Computers use base 2 (binary) internally because electronic circuits have two states: on and off, which map naturally to 1 and 0.
Binary (base 2)
Binary uses only 0 and 1. Each position represents a power of 2: 1, 2, 4, 8, 16, 32, 64, 128... Binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = decimal 10. All data in a computer — text, images, audio, executable code — is ultimately stored and processed as binary. Understanding binary is foundational to understanding computing at a hardware level.
Hexadecimal (base 16)
Hexadecimal uses digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Each position represents a power of 16. Hex is pervasive in computing because one hex digit represents exactly four binary bits, making it a compact and readable representation of binary data. Hex colour codes (#FF6B6B), memory addresses (0x7FFFFFFF), and byte values in network packets are all expressed in hex.
Octal (base 8)
Octal uses digits 0–7. Each position represents a power of 8. Octal is less common today but historically important — older computer architectures that used 6-bit, 12-bit, or 24-bit words found octal more natural than hex. Unix file permissions are expressed in octal: chmod 755 means owner=7 (rwx), group=5 (r-x), others=5 (r-x).
How to use the converter
Enter a number in any of the four fields and the other three update instantly. You can type binary, decimal, hex, or octal and see all representations simultaneously. The hex field accepts both lowercase and uppercase letters.
Practical uses for developers
Hex colour conversion is the most common everyday use — converting #FF6B6B to its decimal RGB components (255, 107, 107) for use in CSS or JavaScript. Bitwise operations are much easier to understand in binary. Unix permissions require octal. Memory debugging involves reading hex addresses and values. Network programming involves converting IP addresses and port numbers between representations.