An analog-to-digital converter (ADC) system that converts an analog input signal into a digital output circuit uses a method of shaping a pseudo-random signal such that the ADC system can be used with input signals having wider swings. The ADC system also includes a quantizer having a comparator offset of less than =/-1/4 least significant bit (LSB) in a stage calibrated for gain errors. A method of operating an ADC circuit includes measuring an amplitude and polarity of an input signal voltage and changing characteristics of a pseudo-random signal to ensure that a subsequent stage of the ADC circuit is not saturated. An implementation of the ADC circuit alters the pseudo-random signal based on the amplitude of the input signal such that when the input signal goes close to a positive rail, the pseudo-random signal alternates between a first range, and when the input signal goes close to a negative rail, the pseudo-random signal alternates between a second range.