Number System Converter — Binary, Octal, Decimal, Hex

Hex wins because two digits are exactly one byte

Colour codes, memory addresses, file signatures, hashes — hexadecimal is everywhere in computing, and not because it is elegant or easy to read. Two hex digits express exactly one byte, and that single fact explains every place you meet it.

Positional notation, briefly

In any base, each position is worth the base times the position on its right. Decimal has ten digits, so positions go up in tens. Binary has two, so they double: 11 in binary is three. Hexadecimal needs sixteen digits and borrows A to F for ten through fifteen.

Read a hex number the same way. In F5, the F sits in the sixteens place — fifteen sixteens is 240 — and the 5 is five units, giving 245. Reverse the digits to 5F and it is five sixteens plus fifteen, which is 95. Position matters exactly as it does in decimal.

Why the byte correspondence matters

A byte holds 256 values, 0 to 255. Two hex digits also express 256 values, 00 to FF, because sixteen times sixteen is 256.

Take 255. It is FF in hex, 11111111 in binary, 377 in octal. The hex form is two digits and each one covers exactly four bits, so you can read the bits straight off it. Decimal 255 tells you nothing about the underlying bits at all — there is no clean relationship between a decimal digit and any number of bits, because ten is not a power of two.

That is the whole argument. Hex appears wherever raw bytes do, because it never wastes a digit and never needs padding: every byte is two characters, always.

Colour codes follow directly

Three channels — red, green, blue — one byte each, two hex digits per channel, six digits total. #FF0000 is full red, no green, no blue. The hex to RGB converter switches between the two notations, which describe identical data in different form.

Where binary and octal earn their place

Hex is for storing and reading bytes. Binary is what you want when individual bits carry separate meanings — flags, bitmasks, status registers — because each bit is a separate yes or no and hex hides that behind a digit.

Octal survives almost entirely because three bits map to one octal digit, which is why file permissions are written as three digits. Permissions 755 is nine bits: read, write and execute for the owner, read and execute for group and others. In binary that is 111101101, which is correct and hard to scan. In hex it is 1ED, which obscures the grouping entirely. Three bits per digit is what makes the octal form readable, and it is the only reason the base is still in use.

Whole numbers convert exactly; fractions do not

This is the limit worth understanding. Converting a whole number between bases is exact and reversible — 255 is always FF, always 11111111, with nothing lost either way.

Fractions are different. 0.1 in decimal cannot be written exactly in binary; it repeats forever, in precisely the way one third cannot be written exactly in decimal. It is not a computer being careless and not a rounding bug — it is the same mathematical fact about which fractions terminate in which base.

Which is why 0.1 + 0.2 does not give exactly 0.3 in most programming languages. Neither operand can be stored exactly to begin with, so the sum inherits both errors. This converter handles whole numbers only.

It validates as you type, rejecting digits that are not legal for the base — a 9 in octal, a G in hex — and converts across all four bases at once, in your browser.