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We propose a new partial-scan algorithm, the first to use toggling rates of the flip-flops (analyzed using DSP methods) and Shannon entropy measures of flip-flops to select flip-flops for scan. This improves the testability of the circuit-under-test (CUT). Entropy is maximized throughout the circuit to maximize the information flow (the principle of maximum entropy), which improves testability. We propose using partial-scan for testing, to maximize fault coverage (FC), reduce test volume (TV), reduce test application time (TAT), and reduce test power (TP) but we allow for full-scan during silicon debug. Full-scan is commonly used for testing, to reduce sequential automatic test-pattern generation (ATPG) to the complexity of combinational ATPG, but comes with serious TV, TAT, and TP overheads. Partial-scan significantly reduces circuit delay, when compared to full-scan, because critical flip-flops in the circuit data path do not have the extra hardware for full-scan, and therefore are roughly 5% faster, and use 10% less area. This is particularly critical for microprocessors. The HITEC ATPG program generated results for this new partial-scan algorithm.