The C-Band All-Sky Survey (C-BASS) is an all-sky full-polarization survey at a frequency of 5 GHz, designed to provide data complementary to the all-sky surveys of WMAP and Planck and future CMB B-mode polarization imaging surveys. We describe the design and performance of the digital backend used for the northern part of the survey. In particular we describe the features that efficiently implement the demodulation and filtering required to suppress contaminating signals in the time-ordered data, and the capability for real-time correction of detector non-linearity and receiver balance.