Binary / Hex / Decimal Converter

Only whole numbers are supported; fractional and negative values are outside the standard base notation used here.

A number base describes how many unique digits are available before a new place value is needed. Decimal, the everyday system, uses ten digits (0-9). Binary uses just two (0-1), octal uses eight (0-7), and hexadecimal uses sixteen, borrowing letters A through F to represent 10 through 15.

To convert, the input is first read according to its stated base and converted internally into an ordinary decimal number — for example, binary 1111 becomes decimal 15. From that single decimal value, the converter then rewrites the number in each of the other bases, dividing repeatedly by the target base and reading off the remainders.

Hexadecimal is especially common in computing because two hex digits map cleanly onto one byte (8 bits), making it a compact way to write binary data such as colors, memory addresses, or error codes. This tool only handles whole, non-negative numbers, since fractional and negative values are outside standard base notation.

Entering 255 in decimal converts to 11111111 in binary, 377 in octal, and FF in hexadecimal — a common value because it is the maximum a single byte can hold. Going the other direction, entering FF and selecting hexadecimal as the input base returns 255 in decimal. This pairing shows up constantly in web design, where a color like #FFFFFF (pure white) is really three bytes of 255 each, one for red, green, and blue. By comparison, entering 128 in decimal — the midpoint of a byte's range — converts to 10000000 in binary, 200 in octal, and 80 in hexadecimal, showing how the same quantity can look very different depending on which base is used to write it down. Recognizing these equivalents helps when reading hardware documentation or debugging color values that mix hex codes with plain decimal numbers.