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Application-specific ICs have been traditionally used to support the high computational and data rate requirements in medical ultrasound systems, particularly in receive beamforming. Utilizing the previously developed efficient front-end algorithms, in this paper, we present a simple programmable computing architecture, consisting of a field-programmable gate array (FPGA) and a digital signal processor (DSP), to support core ultrasound signal processing. It was found that 97.3% and 51.8% of the FPGA and DSP resources are, respectively, needed to support all the front-end and back-end processing for B-mode imaging with 64 channels and 120 scanlines per frame at 30 frames/s. These results indicate that this programmable architecture can meet the requirements of low- and medium-level ultrasound machines while providing a flexible platform for supporting the development and deployment of new algorithms and emerging clinical applications.