 Data converter

A data converter translates between an analog quantity and a digital representation. An analog-to-digital converter assigns a code to a measured input; a digital-to-analog converter produces an analog output from a code. The finite code set imposes quantization, while signal sampling determines which times are represented. These are distinct limitations.

For an original ideal model, take an unsigned $N$-bit converter covering $0\le V<V_{\mathrm{FS}}$ with step $\Delta =V_{\mathrm{FS}}/2^N$. Code $k=\lfloor V/\Delta \rfloor$ identifies one interval. Reconstructing at its midpoint gives $\hat{V}=(k+\frac{1}{2})\Delta$ and $|\hat{V}-V|\le \Delta /2$. This bounds the error of an ideal uniform quantizer; the probabilistic uniform quantization error model requires further assumptions about the inputs.^[ref]

An experiment can slowly sweep a known input and record the transition locations between codes. Unequal step sizes, missing codes and gain or offset errors then become distinguishable from the ideal quantization limit. A changing input adds separate questions about settling and the acquisition time. Quoting only the number of bits therefore does not characterize the complete measurement system.