B-modes are special patterns in cosmic microwave background (CMB) polarization. The detection of them is a smoking-gun signature of primordial gravitational waves. The generic strategy of the CMB polarization experiments is to employ a large number of polarimeters for improving the statistics. The Q/U Imaging ExperimenT-II (QUIET-II) has been proposed to detect the B-modes using the worlds largest coherent polarimeter array (2,000 channels). An unique detection technique using QUIETs polarimeters, which is a modula- tion/demodulation scheme, enables us directly extracting the polarization signal. The extracted signal is free from non- polarized components and intrinsic 1/f noise. We developed a data readout system with on-board demodulation functions for the QUIET-II experiment. We employed a master clock strategy. This strategy guarantees phase matching between the modulation by the polarimeters and the demodulation by ADC modules. The single master generates all carrier clocks and distributes them to each module. The developed electronics, clock modules, and the ADC modules fulfill requirements. Tests with a setup similar to that of the real experiment proved that the system works properly. The performance of all system components are validated to be suitable for B-mode measurements.