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This brief presents an 84-dB dynamic range true logarithmic amplifier. Logarithmic ordering in the output is achieved as a function of control parameter X, which in turn is tuned digitally. The result is a digitally controlled data conversion that yields a new type of logarithmic digital-to-analog converter. This 4-bit nonlinear converter has been fabricated in a TSMC 0.18-μm complimentary metal-oxide-semiconductor technology. Measurement results confirm theory and simulations, and display logarithmic transfer characteristics within [-1.36%, 0.84%] output linear error. The integrated circuit has dimensions of 1.5 × 1 mm2 and an average power consumption of 13.2 mW when powered with ±1.65-V supply voltages.