Different biological tissues have different values of electrical resistivity. In EIT (electrical impedance tomography), we try to provide cross-sectional images of a resistivity distribution inside an electrically conducting subject such as the human body mainly for functional imaging. However, it is well known that the image reconstruction problem in EIT is ill-posed and the quality of a reconstructed image highly depends on the measurement error. This requires us to develop a high-performance EIT system. In this paper, we describe the development of a 16-channel digital EIT system including a single constant current source, 16 voltmeters, main controller, and PC. The system was designed and implemented using the FPGA-based digital technology. The current source injects 50KHz sinusoidal current with the THD (total harmonic distortion) of 0.0029% and amplitude stability of 0.022%. The single current source and switching circuit reduce the measurement error associated with imperfect matching of multiple current sources at the expense of a reduced data acquisition time. The digital voltmeter measuring the induced boundary voltage consists of a differential amplifier, ADC, and FPGA (field programmable gate array). The digital phase-sensitive demodulation technique was implemented in the voltmeter to maximize the SNR (signal-to-noise ratio). Experimental results of 16-channel digital voltmeters showed the SNR of 90dB. We used the developed EIT system to reconstruct resistivity images of a saline phantom containing banana objects. Based on the results, we suggest future improvements for a 64-channel muff-frequency EIT system for three-dimensional dynamic imaging of bio-impedance distributions inside the human body.