Abstract: A recirculating remainder analog-to-digital conversion method and apparatus are disclosed for converting an analog signal into a digitally encoded signal representing the analog signal as two or more digits in a selected number base. Conversion is based on employing two gain factors, one dependent on the digital code used for encoding digits, such as a binary code, and the other dependent on the selected number base for the digits, such as decimal, and by selectively amplifying by the gain factors in a predetermined sequence for producing the signals that are recirculated during conversion of the analog signal into the digitally encoded signal. A method and apparatus are also disclosed for nulling errors in recirculating remainder converters introduced by operation of the converter circuitry by transferring signals through the circuitry once at one polarity and again at the opposite polarity during conversion of the analog signal into the digitally encoded signal.