Simulations in vhdlSandbox/biquad/TDF2_llcooly,ipynb plot the values of register values for the transformed direct form II difference equations and confirm that the registers S10 and S20 need not more bits thatn the input/output values.  As a function of the critical frequency of a low pass filter (sampling frequency 10 MHz) is flat.  A 16-bit integer is 15 integer bits plus one sign bit is "nbits.png"

Using then 15 bits in the fractional part gives good noise performance when fLo=1E4, but that degrades for lower values of fLo.  Here in psd.png the x-axis is frequency/fLo for different