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TOOL IDB-SWE-011
Q-format fixed-point

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Engineering tools are available only on desktop screens.

Q-format fixed-point

Float ↔ Qm.n fixed-point. Resolution, range, and integer encoding for DSP, control loops, and MCUs without an FPU.

Bit allocation & representable range Q1.15 · 16-bit
layout format Q1.15 16-bit RANGE −1.0 0 ~1.0 value 0.5 resolution (1 LSB) = 2^-15 = 3.052e-5
Engineering notes

Q-format notation

  • Qm.n: m integer bits + n fraction bits. Total = m + n (+ 1 sign for signed).
  • Q15 = Q1.15 (int16): range [−1, 1−2⁻¹⁵], step 2⁻¹⁵.
  • Q31 = Q1.31 (int32): range [−1, 1−2⁻³¹], step 2⁻³¹.

Encoding

  • int = round(float × 2^n)
  • float = int / 2^n
  • Saturate at min/max to avoid overflow wrap-around.

Result

Live