Fixed-point converter

Float ↔ fixed in any Q-format. Pick a word width and Q-factor — the integer-bits exponent E, the value range and the LSB follow — then convert a value with your choice of rounding and saturation.

The Q-format

For a signed N-bit type the Q-factor (fractional bits) and the integer-bits exponent E satisfy E = (N − 1) − Q. Edit either field — the other follows.

Data type

Q (fractional bits)

E (integer bits)

Convert a value

Rounding

Float value

Bulk mode (comma- or whitespace-separated)

Floats

What the result means

Range: the smallest and largest float values the format can represent.
LSB: 2^−Q — one integer step expressed as a float.
1.0 ↔ int: 2^Q — the integer that represents 1.0, useful when reading raw memory dumps.
Conceptual integer: round(x · 2^Q) before saturation. May be outside the type's range.
Saturated integer: clamped to [−2^N−1, 2^N−1−1]. The SAT flag indicates whether saturation actually fired.
Hex: two's-complement representation in N bits (matches what you'd see in a memory dump).
Round-trip: the saturated integer divided back by 2^Q.
Error / LSBs: round-trip − x, both as a float and as a multiple of the LSB (2^−Q).

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