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Applications such as brain-machine interfaces require hardware spike sorting in order to 1) obtain single-unit activity and 2) perform data reduction for wireless data transmission. Such systems must be low-power, low-area, high-accuracy, automatic, and able to operate in real time. Several detection, feature-extraction, and dimensionality-reduction algorithms for spike sorting are described and evaluated in terms of accuracy versus complexity. The nonlinear energy operator is chosen as the optimal spike-detection algorithm, being most robust over noise and relatively simple. Discrete derivatives is chosen as the optimal feature-extraction method, maintaining high accuracy across signal-to-noise ratios with a complexity orders of magnitude less than that of traditional methods such as principal-component analysis. We introduce the maximum-difference algorithm, which is shown to be the best dimensionality-reduction method for hardware spike sorting.