Qm.n is a signed fixed-point format with m integer bits and n fractional bits, plus one sign bit, giving m+n+1 total bits. The stored integer equals the real value multiplied by 2 to the power n.

How is the binary value computed?

The tool multiplies your number by 2^n, rounds to the nearest integer, then encodes that as a two's-complement integer of m+n+1 bits. This is the exact pattern stored in a register.

What is the resolution of a fixed-point format?

The smallest representable step is 2 to the power minus n. More fractional bits (larger n) give finer resolution but a smaller integer range for the same total width.

Why does my value show a quantization error?

Fixed-point can only represent multiples of its resolution. If your number falls between two steps it is rounded, and the difference is the quantization error the tool reports.

Is this calculation done online?

No. Everything is computed locally in your browser using JavaScript. Nothing is uploaded, so the tool is private and works offline once loaded.

Fixed-Point Converter

Fixed-point representation stores fractional numbers as plain integers by agreeing on an implicit scaling factor. It is the workhorse of digital signal processing (DSP), embedded firmware and FPGA designs, where floating-point hardware is expensive or absent. This converter encodes any decimal into a signed Qm.n format and shows you the exact bits.

How it works

A signed Qm.n number reserves:

1 sign bit,
m bits for the integer part,
n bits for the fractional part,

for a total of m + n + 1 bits. To encode a value:

Multiply the real value by 2^n (the scaling factor).
Round to the nearest integer — this is the stored integer.
Interpret that integer as a two’s-complement number of m + n + 1 bits.

To decode, you divide the stored integer by 2^n. The smallest representable step (resolution) is 2^-n, and the representable range is [-2^m, 2^m - 2^-n].

Example

Encoding 3.14159 in Q7.8 (16 bits total): multiply by 2^8 = 256 to get 804.24, round to 804. Decoding, 804 / 256 = 3.140625, so the quantization error is about -0.000965. Adding more fractional bits shrinks that error at the cost of integer range.

Notes

If your value exceeds the representable range the tool flags an overflow and clamps the result, mirroring what a saturating fixed-point unit would do. Choose m and n to balance the magnitude you need against the precision you need.