Numbers Converter

Convert numbers between binary, decimal, hexadecimal, and octal, with how each numbering system actually works explained.

How Binary, Decimal, and Hexadecimal Are Really Just Different Counting Bases

Every number system humans use, decimal, binary, or hexadecimal, works on exactly the same underlying logic, positional place value, where each digit’s position represents a power of the system’s base, and the only thing that actually changes between systems is what that base number is. Decimal, the everyday system, uses base ten because humans have ten fingers, meaning each position represents a power of ten, so the number present in the “tens” position is worth ten times more than the same digit in the “units” position. Binary, the language computers fundamentally operate in, uses base two, meaning only the digits zero and one exist, and each position represents a power of two rather than ten, which maps directly onto the on-or-off electrical states a computer’s circuits actually use, making binary the natural, not arbitrary, choice for digital systems. Hexadecimal, base sixteen, exists specifically as a human-friendly shorthand for binary, because each single hexadecimal digit represents exactly four binary digits, making a long, unwieldy binary number dramatically shorter and easier to read once converted to hexadecimal, which is exactly why colour codes in web design and memory addresses in programming are almost always written in hexadecimal rather than raw binary, despite the underlying computer still working entirely in binary beneath that human-readable layer.