I am working on a system that is implementing a digital filter that was designed for another system that had an FPU and a 12bit ADC. The system that I am working on is using the same filter without an FPU using a 12 ADC and fixed point arithmetic.
The ADC resolution is 3.3v / 2^12 = 0.000805664062v
With an FPU each ADC integer value could be scaled with the above resolution.
On the system using fixed point where
m2^-e, e = 10
The resolution would be
2^-10 = 0.0009765625
This leads me to think that the use of fixed point is giving me slightly lower resolution.
Looking at it differently and representing a delta between ADC integers with 14bits for the fraction the resolution could be
2^(-11) + 2^(-12) + 2^(-14) = 0.000793457031
but then the range would be perceived as less than 3.3V
Is this thinking correct?