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A variable-resolution (VR) quantizer with input-activity-dependent adjustable resolution is presented. Several potential schemes are discussed; the favored scheme achieves adjustable resolution by level skipping according to the speed of the input. The advantages of a VR analog-to-digital conversion (ADC) are presented with applications in continuous-time (CT) digital signal processing systems. It is shown that a decrease in resolution for fast inputs does not corrupt the in-band spectrum while leading to a reduction in the number of samples produced by a CT ADC. The result is a significant decrease in power dissipation but without in-band performance degradation. Analysis and extensive simulations are provided. Simulations using signals in the voice band show that a power reduction of over 80% is achievable with a VR quantization.