This paper proposes an adaptive algorithm for a predicting SAR ADC which can self-adjust the precision of its prediction. A precise and yet correct prediction reduces bit trials needed in a SAR conversion, leading to great power savings. The presented algorithm uses a 2-byte prediction-success-rate-register and a1^st order digital negative feedback loop to control the prediction depth. Additionally, an offset-move-up technique is proposed to boost the prediction success rate when the previous sample is near the boundary of the predicted subrange. The boundary-crossing problem reduces energy-efficiency in other predictive SAR algorithms such as LSB-first. The proposed scheme makes aggressive predictions for low-activity biomedical signals, makes conservative predictions or no predictions for high-activity-high-amplitude signals and it automatically and smoothly transitions between the two extremes.