The CEBAF accelerator at Jefferson Lab is currently using an analog beam current monitoring (BCM) system for its machine protection system (MPS), which has a loss accuracy of 2 µA. Recent burn-through simulations predict catastrophic beam line component failures below 1 µA of loss, resulting in a blind spot for the MPS. Revised MPS requirements target an ultimate beam loss accuracy of 250 nA. A new beam current monitoring system has been developed which utilizes modern digital receiver technology and digital signal processing concepts. The receiver employs a direct-digital down converter integrated circuit, mated with a Jefferson Lab digital signal processor VME card. Adaptive filtering is used to take advantage of current-dependent burn through rates. Benefits of such a system include elimination of DC offsets, generic algorithm development, extensive filter options, and interfaces to UNIX -based control systems.