 Solution

For a real signal with highest frequency $f_{\max }=40\mathrm{MHz}$, the Nyquist–Shannon sampling theorem gives the nominal Nyquist sampling rateTo cover an arbitrary component exactly at the band edge, choose $f_s>80\mathrm{MHz}$: a $40\mathrm{MHz}$ sine sampled at exactly $80\mathrm{MHz}$ can have every sample equal to zero for an unfortunate phase. Practical aliasing suppression also calls for a margin above the nominal limiting rate.

With rounding to the nearest digitizer level, quantization with step $q=0.1\mathrm{mV}$ has the uniform-quantization error boundThus the stated digitizer meets the requested nominal amplitude precision per sample, assuming no clipping or other errors. The bandwidth sets the nominal minimum sampling rate; the level spacing sets the rounding precision. Strictly, the sampling theorem reconstructs exactly from exact samples. A uniform $0.05\mathrm{mV}$ error bound on the entire reconstructed continuous waveform is not guaranteed by the level spacing and sampling rate alone; that stronger requirement needs a specified reconstruction and noise model.