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Single-pixel transition-edge sensors (TES) are useful for a variety of applications requiring the detection of photons from sub-millimeter wavelengths to gamma rays. Arrays of TES's are required in the next-generation instruments to continue to be useful. We report on the development and performance of an electronics system used to readout and process signals from arrays of TES detectors. The system utilizes high-performance analog and digital electronics, and digital signal-processing. Because the system digitizes signals early in the signal processing chain, it is possible to implement a digital-feedback system to flux lock a SQUID amplifier and digitally process the detector (feedback) signal.