Hex Fraction to Decimal Converter

Sixteenths and beyond

Hex digits continue past the point with negative powers of sixteen: the first fractional place is 1/16, then 1/256. A hex fraction is the sum of those weighted digits — and because 16 is a power of two, every finite hex fraction converts to an exact, finite decimal.

Hex fractions are the compact notation for binary fractions — one digit carries four fractional bits — which is why float literals and fixed-point registers are often documented this way.

Worked example

Input: A.4

Integer:  A = 10
Fraction: 4/16 = 0.25

Result: 10.25  (exact)

The fractional place table

Connections to floating point

C’s hexadecimal float literals (0x1.8p1 = 3.0) exist precisely because hex fractions map losslessly onto binary mantissas — no decimal rounding ambiguity. Reading an IEEE-754 mantissa in hex and converting it here reproduces the exact stored value, which the IEEE-754 converter then confirms field by field.

Guarantees and privacy

Always exact: n hex places produce at most 4n decimal places, computed rationally. Errors are positional; the only structural rule is a single point. As throughout the cluster, the value never leaves your browser.

Hex fractions are binary fractions in disguise

Because 16 is 2⁴, every hex digit after the point is exactly four binary fraction bits, so a hex fraction terminates precisely when its binary equivalent does: 0.8₁₆ is 0.5 and 0.4₁₆ is 0.25. This is why C’s hexadecimal floating-point literals and the printf %a format exist — a value like 0x1.8p1, meaning 1.5 times two, is exactly 3.0, and hex notation can write any float or double exactly, which decimal often cannot.