This binary fraction converter converts decimal fractions to binary fractions and binary fractions back to decimal, with selectable display precision.
Math
Binary Fraction Converter
Convert between decimal and binary fractions with selectable digit count.
Calculator
About this calculator
Formula notes
A binary fraction uses negative powers of two: 0.1₂ = 1/2, 0.01₂ = 1/4; the converter expands or collects these terms with a chosen number of bits.
Worked examples
- Example: decimal 0.5 equals binary 0.1; decimal 0.75 equals binary 0.11.
- Decimal 0.625 equals binary 0.101, because 1/2 + 1/8 = 0.625.
How to use it
- Choose whether converting from decimal to binary or from binary to decimal.
- Enter the fraction value in the active field.
- Read the converted result at the selected digit precision.
Frequently asked questions
Why does 0.1 decimal not have a short binary form?
Many decimal fractions repeat in binary. The converter rounds to the selected number of digits, which can introduce a small rounding difference.
Can I set more bits?
Yes. Choose 4, 8, 12, 16, or custom digit precision to balance readability and accuracy.
Limits and interpretation
- Binary fractions can be non-terminating; the chosen digit precision introduces rounding error.
- The converter follows the standard binary place-value interpretation, which may differ from floating-point display conventions in programming languages.