We have built a high precision (24-bit) data acquisition (DAQ) system capable of simultaneously sampling eight input channels for the measurement of the electric dipole moment of the electron. The DAQ system consists of two main components: a master board for DAQ control and eight individual analog-to-digital converter (ADC) boards for signal processing. This custom DAQ system provides galvanic isolation of the ADC boards from each other and the master board using fiber optic communication to reduce the possibility of ground loop pickup and attain ultimate low levels of channel cross-talk. In this paper, we describe the implementation of the DAQ system and scrutinize its performance.