IceCube is a km-scale neutrino observatory under construction at the South Pole with sensors both in the deep ice (InIce) and on the surface (IceTop). The sensors, called Digital Optical Modules (DOMs), detect, digitize and timestamp the signals from optical Cherenkov-radiation photons. The DOM Main Board (MB) data acquisition subsystem is connected to the central DAQ in the IceCube Laboratory (ICL) by a single twisted copper wire-pair and transmits packetized data on demand. Time calibration is maintained throughout the array by regular transmission to the DOMs of precisely timed analog signals, synchronized to a central GPS-disciplined clock. The design goals and consequent features, functional capabilities, and initial performance of the DOM MB, and the operation of a combined array of DOMs as a system, are described here. Experience with the first InIce strings and the IceTop stations indicates that the system design and performance goals have been achieved.