Binary Fraction
Convert binary numbers with fractional points to decimal values with this free binary fraction calculator. Handles integer and fractional binary parts with high precision.
About This Calculator
The binary fraction calculator converts binary numbers with fractional parts (numbers containing a binary point) into their decimal equivalents. Binary fractions use negative powers of two for digits after the binary point, just as decimal fractions use negative powers of ten after the decimal point.
To convert a binary fraction manually, separate the integer and fractional parts at the binary point. For the integer part, multiply each bit by 2 raised to its position index starting from 0 at the rightmost integer digit. For the fractional part, multiply each bit by 2 raised to the negative power of its position index starting from -1 at the first fractional digit. Sum all values where the bit is 1.
For example, the binary number 101.101 converts to decimal as: (1x4 + 0x2 + 1x1) + (1x0.5 + 0x0.25 + 1x0.125) = 5 + 0.625 = 5.625. This calculator is ideal for students learning number systems, programmers working with binary data, and electronics engineers dealing with fixed-point or floating-point arithmetic.
Frequently Asked Questions
How do you convert a binary fraction to decimal?
To convert a binary fraction to decimal, split the number at the binary point. The integer part uses powers of 2 from right to left (1, 2, 4, 8...). The fractional part uses negative powers of 2 from left to right (1/2, 1/4, 1/8...). Sum all position values that contain a 1 bit.
What is the binary point?
The binary point is the binary equivalent of the decimal point. Digits to the left represent integer values (2^0, 2^1, 2^2...), while digits to the right represent fractional values (2^-1, 2^-2, 2^-3...). For example, 101.101 in binary equals 5.625 in decimal.
Can this calculator handle binary numbers without a fraction point?
Yes, if you enter a binary number without a fractional point (e.g. 1010), the calculator treats it as a pure integer and converts only the integer part to decimal.
Why use binary fractions?
Binary fractions are fundamental in digital computing for representing non-integer values. They are used in floating-point arithmetic, digital signal processing, scientific computing, and any application where fractional values need precise binary representation.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use with no registration or subscription required.
How many decimal places does the result show?
The decimal result is displayed with up to 10 decimal places for maximum precision. Binary fractions with many fractional bits may produce repeating decimal fractions, which are shown with the available precision.