A sigma-delta modulation sensing circuit and an analog-to-digital converter for an imager that eliminate the erroneous conversion of non-zero analog voltages to zero digital voltages is provided. The sensing circuit includes an offset branch that allows input of an offset voltage that is at least as large as a negative channel-specific offset found in a pixel signal voltage. The sensing circuit also includes a regulation branch based on a reference voltage common across multiple columns of an imager. The regulation branch has an adjustable resistance that is modulated during the sensing operation, which creates an adjustment current that is applied during the sensing operation to a reset signal. The sensing circuit and analog-to-digital converter generate digital code based on the difference between the reset voltage and the summed offset and pixel signal voltage.