In this paper, an algorithm of the median-cut quantization (MCQ) is proposed. MCQ is the technique that reduces multi-valued samples to binary-valued ones by adaptively taking the median value as the threshold. In this work, the search process of the median value is derived from the quick-sort algorithm. The proposed algorithm searches the median value bit by bit, and samples are quantized during the search process. Firstly, the bit-serial procedure is shown, and then it is modified to the bit-parallel procedure. The extension to the multi-level quantization is also discussed. Since the proposed algorithm is based on bit operations, it is suitable for hardware implementation. Thus, its hardware architecture is also proposed. To verify the significance, for the application to the motion estimation, the performance is estimated from the synthesis result of the VHDL model.