Disclosed herein are systems and methods that describe statistical estimation based noise reduction for SAR ADCs. For SAR ADCs, the conversion error can be available at the comparator input. Although a noisy 1-bit comparator may not be able to produce an accurate estimation for its input if used only once, the comparison can be repeated multiple times for a designated bit of the multi-bit SAR ADC. This can allow for the improvement of the estimation accuracy by examining the probability of the comparator output being “1” or “0”. The estimation of a signal from a noisy environment using multiple trials can be cast as a classic statistical estimation issue. In one aspect of the disclosure, an optimal Bayes estimator is disclosed to achieve a low estimation error from the comparator on a designated bit of the multi-bit SAR ADC.