This fully digital beam position measurement instrument is designed for beam position monitoring and machine research in Shanghai Synchrotron Radiation Facility.The signals received from four position-sensitive detectors are narrow pulses with a repetition rate up to 499.654 MHz and a pulse width of around 100 ps,and their dynamic range could vary over more than 40 dB in machine research.By the employment of the under-sampling technique based on high-speed high-resolution A/D conversion,all the processing procedure is performed fully by the digital signal processing algorithms integrated in one single Field Programmable Gate Array.This system functions well in the laboratory and commissioning tests,demonstrating a position resolution (at the turn by turn rate of 694 kHz)better than 7 μm over the input amplitude range of-40 dBm to 10 dBm which is well beyond the requirement.