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We describe a new approach to Johnson noise thermometry (JNT) that takes advantage of the recent advances in Josephson voltage standards and digital signal processing techniques. Previous attempts at high-precision thermometry using Johnson noise have been limited by the non-ideal performance of the electronic systems. By using the perfect quantization of voltages from the Josephson effect, any arbitrary broadband waveform can be synthesized and used as a calculable noise source for calibrating the cross-correlation electronics. With better calibration, we should be able to achieve relative accuracies of parts in 10/sup 5/ for an arbitrary temperature in the range between 84 K and 430 K. We present the latest measurements of our recently constructed JNT system.