How this works. Fixed point stores a fraction as a plain integer with an implied
binary point: in
Qm.n the raw integer is the real value multiplied by
2n, so the hardware only ever does integer arithmetic. Resolution is
constant at
2−n across the whole range — unlike floating point, which
trades precision for range as the magnitude grows. That constant step is exactly why control
loops and DSP filters prefer it. For signed formats the sign bit takes one bit from the integer
part, which is why Q15 holds values in
−1 … 0.999969482421875 and cannot represent
+1. Conversion rounds half away from zero, and values outside the range clip
rather than wrap.
This value is outside the representable range for the chosen format and has been clipped — in a real system this is saturation, and it silently distorts the signal.