One can construct a successive-approximation analog-to-digital converter (ADC) whose output is proportional to the logarithm of the input voltage, by using independent electronically switched attenuators. The output step size of such an ADC corresponds to a constant relative change in the voltage being measured, rather than a constant absolute change as in a linear ADC. The principle described here is fully ''digital'' in that it depends only on the accuracy of resistors and not on the logarithmic I-V characteristic of any solid-state device. A practical ten-bit prototype conforms to the ideal logarithmic characteristic to about 1% over a four-decade input voltage range, 1 mV to 10 V; effectively, any input in that range is measured to about 1%. Complexity, cost, and speed are comparable to simple linear ADCs.