We have built a cryogenic current comparator (CCC) resistance bridge for the comparison of standard resistors in the range of 1 Omega-100 kOmega. The use of fully programmable current sources allows for smooth polarity reversals, regardless of the time constant of each side of the bridge. We measured a CCC transfer function of 2.25 muA middotturn/phi₀ and a noise level of 54 pA middot turn/radic(Hz) at 1 Hz, with a 1/f corner of about 0.6 Hz. Two different readout schemes were implemented and compared with good agreement. We performed a few measurements to assess the accuracy of the bridge and evaluated all the significant sources of error. The total uncertainty of the bridge is estimated to be 2.6 parts in 10⁹ between 1 Omega and 10 kOmega.