Math

Instant, private, and free

Binary Fraction Calculator.

Convert a finite binary fraction to decimal.

On-device calculationNo signup
01

Set your values

Results update as you type.

Decimal value: 0.625

Decimal value

0.000000

Results update automatically as you type.

Use Cases

Learning binary arithmetic

Students can verify their manual conversions of binary fractions to decimal, reinforcing understanding of base-2 positional notation.

Example: Check that 0.101 equals 0.625 in decimal.

Programming and digital systems

Developers and engineers often need to interpret binary fractions from low-level data or hardware specifications. This tool provides quick conversion.

Example: Convert 1101.011 to decimal for a fixed-point value.

Frequently Asked Questions

What is a binary fraction?
A binary fraction is a number expressed in base-2 with a fractional part, using only 0s and 1s, with a binary point (similar to a decimal point). For example, 101.101 represents 5.625 in decimal.
How do you convert a binary fraction to decimal?
Separate the integer and fractional parts. For the integer part, multiply each digit by 2 raised to its position (from right to left, starting at 0). For the fractional part, multiply each digit by 2 raised to negative powers (from left to right, starting at -1). Sum all results.
Can this calculator convert any binary fraction?
It converts finite binary fractions. If you enter a binary fraction with a finite number of digits after the binary point, it will give the exact decimal equivalent. It does not handle infinite repeating binary fractions.

Tips & Common Mistakes

Tips

  • Ensure you use only 0 and 1 digits. Any other character will cause an error.
  • The binary point is optional. If you enter a whole binary number, it will be treated as an integer.
  • For fractional parts, the more digits you include, the more precise the decimal representation will be.
  • Double-check the placement of the binary point; it determines the value of each fractional digit.

Common Mistakes to Avoid

  • Using a decimal point instead of a binary point. The calculator expects a dot (.) as the separator.
  • Including spaces or commas in the binary fraction, which are not valid characters.
  • Entering a binary fraction with a repeating pattern (like 0.101010...) – this calculator only handles finite fractions.

Last updated: August 13, 2026