Binary Fraction Calculator
Convert a binary fraction such as 101.101 into its decimal value. Enter a binary number with an optional point, and this calculator adds the integer part to the fractional part, where each bit after the point is worth 1/2, 1/4, 1/8, and so on.
Formula
decimal = integer part(base-2) + Σ (fraction bit × 2^−position)
- The digits before the binary point are read as an ordinary binary integer.
- Each digit after the point is worth a negative power of two: the first is 1/2 (0.5), the second 1/4 (0.25), the third 1/8 (0.125), and so on.
- The decimal value is the integer part plus the sum of the fractional bit weights.
- Enter only the digits 0 and 1 with at most one point. A leading '0b' prefix is accepted and ignored.
- Many binary fractions do not terminate in decimal, so the result is rounded to six decimal places.
101.101 in decimal
Inputs
- Binary Fraction: 101.101
The integer part 101₂ = 5. The fraction .101 = 1×0.5 + 0×0.25 + 1×0.125 = 0.625. Total = 5.625.
Frequently asked questions
What is a binary fraction?
A binary fraction is a base-2 number with a point, where digits after the point represent halves, quarters, eighths, and so on — the binary equivalent of a decimal point.
How do I read the digits after the point?
Each position after the point is worth 2 raised to a negative power: 2⁻¹ = 0.5, 2⁻² = 0.25, 2⁻³ = 0.125, and so on. Add the weights wherever the bit is 1.
Do I need the integer part?
No. You can enter a pure fraction like .101 or a whole-and-fraction value like 101.101 — the calculator handles both.
Why is the result rounded?
Some binary fractions, like 0.1₂ repeating, have no exact finite decimal form, so the result is rounded to six decimal places for readability.
Can I enter a '0b' prefix?
Yes. A leading 0b is removed automatically, so 0b101.101 and 101.101 give the same result.