Emulating memristor via FPGA offers flexibility for quick prototyping and design space exploration because memristor manufacture and integration are currently insufficient for large-scale application in neural networks. Although important, the creation of fast and lightweight FPGA memristor emulators is still very difficult. In this work, a reconfigurable memristor emulator that can be implemented in digital circuits is proposed. With less than 1% hardware utilization and a 258 MHz operating frequency, the suggested solution has been successfully synthesized and confirmed on a Xilinx ZYNQ-7000 FPGA. Additionally, this work builds a memristor crossbar array for extracting digital picture information and then performs the digital recognition task using a quantitative artificial neural network in order to assess the synaptic function of the suggested memristor model. The experimental results show that the recognition accuracy of MNIST dataset images by the memristor network circuit reaches 91.89%.