Fixed Point (Q-Format) Converter
Convert between floating-point and signed Qm.n fixed-point representation.
Q-Format Fixed-Point represents fractional numbers using pure integers, which is vital for high-speed DSP operations on MCUs without a hardware FPU.
Formulas:
- Scale Factor:
2^n - Fixed-Point Value:
Round(Float * 2^n) - Float equivalent:
Fixed_Value / 2^n
Usage: Input the number of integer bits (m) and fractional bits (n), then enter either a floating-point value or a raw integer to convert bidirectionally.
When you need it: Doing DSP, PID or sensor-scaling math on an MCU without an FPU — representing fractions as scaled integers (Q15, Q1.15) so filters and control loops run fast in integer arithmetic.
Worked example: In Q15 (15 fractional bits) 0.75 → 0.75 × 32768 = 24576 (0x6000). The resolution is 1 / 32768 ≈ 3.05e-5 and the representable range of Q1.15 is [−1.0, +0.99997].
Tips & gotchas:
- Multiplying two Qn values gives a Q2n result — shift right by n to renormalise back to Qn.
- Guard against overflow: accumulate in a wider type (e.g. 32-bit for Q15 products) or use saturating math.
- Q15 cannot represent exactly +1.0; scale your coefficients so they stay below full-scale.
- Round before truncating (add half an LSB) to avoid a consistent downward bias in long sums.