= Solution
A small constant input can repeatedly produce the same <analogue-to-digital converter> code, so averaging those codes cannot reveal its position within a conversion interval. <dither> makes adjacent codes toggle; their relative <frequencies> then encode changes smaller than one conversion step. With adequate <oversampling>, low-pass filtering and averaging reduce the added, sufficiently uncorrelated <noise> while retaining the slow <signal>.
For independent sample errors, the averaged <standard deviation> scales as $N^{-1/2}$; ideally four times as many samples gain about one effective bit. For example a constant input $0.2\Delta$ rounded to levels separated by $\Delta$ would always return zero. Adding uniform <dither> on $[-\Delta/2,\Delta/2]$ gives output $\Delta$ with <probability> $0.2$ and zero otherwise: the expected average is $0.2\Delta$, with error $0.4\Delta/\sqrt N$. The benefit concerns the filtered estimate, not a more accurate individual conversion. Excessive <dither> wastes range, and averaging does not correct calibration bias, correlated drift or arbitrary converter nonlinearity.<AN-1549: Performance Optimization of the Integrated ADC on the ADuCM4050 by Analog Devices>[Oversampling and Averaging, especially the dither and uncorrelated-noise discussion; Table 1]{ref}
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