The design considerations for a completely digitally controlled cryogenic current comparator resistance ratio bridge, including the feedback loops for voltage and current balance, are described. The numerical algorithms have been modeled and optimized, and the overall system performance is illustrated with example measurement data. It is shown that the final performance of the bridge is limited only by the accuracy of the current comparator, the noise sources associated with the current and voltage null detectors, and the resistors under test. An explanation of how the effect of leakage resistance in the system is minimized is also given.