We describe a digitally programmable impedance bridge, used here for low‐temperature resistance thermometry, and a compatible digital programming and data logging interface. The bridge employs a commercial programmable ratio transformer to achieve high resolution with minimum circuit complexity. We measure the ratio of the resistances of a carbon thermometer and a fixed reference resistor, both near 2 K, with a resolution limited by Johnson noise in the resistors. The bridge circuit described here is suitable for a variety of programmable or self‐balancing impedance measurements.