<p>Bunch-by-bunch beam parameter monitors play a crucial role in the measurement system of particle accelerators. Beam position measurement (BPM) is a fundamental function of any beam measurement system and is vital for the overall performance of the accelerator. The BPM electronics equipment is capable of acquiring different types of beam position measurement data at various acquisition rates. Generally, these data types can be classified into four categories: closed-orbit data, fast acquisition data, turn-by-turn data, and bunch-by-bunch data. Among these, the bunch-by-bunch data type corresponds to the highest sampling rate of the BPM electronics. It provides more detailed beam position information, which is particularly useful for in-depth physical analysis of the behavior of the accelerator. In this study, a bunch-by-bunch digital BPM system was developed using BEPC-II as the platform. An experimental validation of beam instability study was conducted in BEPC-II. The bunch-by-bunch system consists of hardware, firmware, and application software. It enables the measurement of individual bunch positions and currents, as well as the tracking and comparison of any bunch in the storage ring for thousands of turns. The system also facilitates basic data analysis, such as generating x-y-t 3D plots in the time domain, identifying the envelope curve, fitting the instability growth time, etc. Additionally, it allows analysis in the frequency domain to determine the mode number, identify the tune, detect the most unstable mode, and more. Overall, the bunch-by-bunch digital BPM system provides a comprehensive solution for precise beam position measurement and detailed analysis of beam instabilities in particle accelerators.</p>