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A quantizer that must accommodate a wide range of signal powers would ordinarily require a large number of output levels compared to a quantizer of signals with known power. In this paper a quantizlng scheme is described for situations in which the signal power is unknown a priori but remains constant for the duration of a communication. The required number of levels is reduced because the quantizer amplitude range is adjusted during an initial training period to the value appropriate to the current signal power. At each sample time during the training period, the amplitude range is adjusted by a multiplicative quantity that depends on the most recent quantized output and upon the time elapsed since the onset of training. Assuming independent identically distributed inputs, it is shown that the quantizer range converges to a fixed multiple of the rms value of the input. The ratio of final range to rms input is a unique function of the multipliers, and a formula is presented that allows a designer to choose multipliers that result in any desired range-to-signal ratio. For each final ratio, there are many sets of multipliers, and formulas are derived that indicate, for a limited training period, the tradeoff between the accuracy of the quantizer range and the size of the set of signal powers to which the quantizer can adapt. Computer simulations illustrate the effects of particular multiplier sequences.