Bit-depth requirements for waveform digitization

A full-scale range $V_{\mathrm{FS}}$ and allowed quantization step $\Delta$ require $b\ge \lceil {\log }_2(V_{\mathrm{FS}}/\Delta )\rceil$ bits. The ideal uniform-quantizer rms error is approximately $\Delta /\sqrt{12}$. Bandwidth determines the sampling-rate requirement, but does not by itself determine a bit depth.