This paper introduces a novel arithmetic tracking algorithm for successive approximation ADCs, and presents its analysis. The algorithm utilizes low activity signal periods to cut the ADC energy dissipation by reducing the number of required bit-cycles. The approach determines the required step size, and bypasses conversion cycles when signal activity is low, without compromising the precision or sampling rate. The required first-order predictions and boundary checkings are performed with simple digital circuits. A lowered number of cycles paired with reduced voltage variations across DAC capacitors yields power savings. The solution has been simulated in a 90 nm CMOS process using HSPICE, demonstrating a 10-bit tracking SAR ADC. The proposed ADC was examined with low activity signals such as EEG, ECG, etc. The results predict from 5.8 µW to 27.6 µW dissipation when the sampling rates range from 32 kHz to 800 kHz, respectively.