Number Base Converter

Number bases are numeral systems that use a certain number of digits. Base 10 (decimal) uses digits 0-9 and is the one used daily. Base 2 (binary) uses only 0 and 1 and is the language of computers. Base 8 (octal) uses 0-7, and base 16 (hexadecimal) uses 0-9 and A-F for web colors, memory addresses and programming.

To convert a number from one base to another, you generally go through base 10. For example, binary 1010 equals 1x8 + 0x4 + 1x2 + 0x1 = 10 in decimal, which becomes A in hexadecimal. Each digit represents a power of the base: in binary powers of 2, in octal powers of 8, in hexadecimal powers of 16.

Hexadecimal is fundamental in computing because each hex digit corresponds exactly to 4 binary bits, making conversion immediate. It is used for CSS colors (#FF5733), memory addresses (0x7FFF), RGB values, character encodings (UTF-8) and binary data debugging. It is much more compact than binary: FF is more readable than 11111111.

Decimal, binary with base two, octal with base eight and hexadecimal with base sixteen. Entering a number in any of them fills in the other three at once, so you can read the same value four ways.

Because one hexadecimal digit stands for exactly four binary digits, so a byte fits into two characters. It is shorter than binary to write and maps onto it without arithmetic, which is why colours and memory addresses use it.

Binary takes only 0 and 1, octal 0 to 7, decimal 0 to 9 and hexadecimal 0 to 9 plus the letters A to F. A character outside the range for that base makes the number invalid rather than being ignored.

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