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This paper describes a new method of pulse compression, the binary power multiplier (BPM), a device which multiplies RF power in binary steps. It comprises one or more stages, each of which doubles the input power and halves the input pulse length. Practical designs are described and expressions for their compression efficiency are derived. The usefulness of pulse compression for accelerator design is illustrated and compared with the pulse compression system currently in use at the Stanford Linear Accelerator Center.