Fixed-Point Math Calculator

Pick Q formats for each input and the output. See the raw integers, the stored real value, and the quantization error, live.

Fixed-Point Math Calculator

Pick a Q format for each input. For multiply and divide, pick the shift count N - the output Q is computed from qA, qB, and N. Add and subtract require both operands in the same Q.

Raw int: 20971520 = 20971520 / 2^24

Stored as: 1.250000000

Quant error: 0.000000%

Q24: range +/-128, LSB 5.96e-8

Raw int: 10923 = 10923 / 2^15

Stored as: 0.3333435059

Quant error: 0.0032%

Q15: range +/-65536, LSB 0.0000305

Shift count N in _IQNmpy:

Output Q = Q24qA + qB - N = 24 + 15 - 15 = 24 - follows A's Q

C code

IQmath style

_IQ15mpy(_IQ24(1.25), _IQ15(0.333333));   // result Q24

Result

0.4166793823

Ideal (real): 0.416666250000

Raw int (Q24): 6990720

Total error vs real math: 0.0032%

Uses signed-32-bit storage. Values above a format’s range clamp to Int32 bounds. Multiplication uses BigInt internally for full 64-bit precision before the right-shift back to the output Q.

For a walkthrough of what Q formats are, how addition/multiplication/division actually work at the bit level, and why mixing IQNmpy with IQNdiv wisely matters, read the fixed-point math guide.