This paper describes an algorithm for Successive Approximation Register (SAR) ADCs with overlapping steps that allow comparison decision errors (due to, such as DAC incomplete settling) to be digitally corrected. We generalize this non-binary search algorithm, and clarify which decision errors it can digitally correct. This algorithm requires more SAR ADC conversion steps than a binary search algorithm, but we show that the sampling speed of an SAR ADC using this algorithm can be faster than that of a conventional binary-search SAR ADC — because the latter must wait for the settling time of the DAC inside the SAR ADC. key words: SAR ADC, digital error correction, non-binary, redundancy