This paper presents a fully digital implementation of a memristor hardware simulator, as the core of an emulator, based on a behavioral model of voltage-controlled threshold-type bipolar memristors. Compared to other analog solutions, the proposed digital design is compact, easily reconfigurable, demonstrates very good matching with the mathematical model on which it is based, and complies with all the required features for memristor emulators. We validated its functionality using Altera Quartus II and ModelSim tools targeting low-cost yet powerful field programmable gate array (FPGA) families. We tested its suitability for complex memristive circuits as well as its synapse functioning in artificial neural networks (ANNs), implementing examples of associative memory and unsupervised learning of spatio-temporal correlations in parallel input streams using a simplified STDP. We provide the full circuit schematics of all our digital circuit designs and comment on the required hardware resources and their scaling trends, thus presenting a design framework for applications based on our hardware simulator.