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Reverse-engineering the brain is one of the US National Academy of Engineering’s “Grand Challenges.” The structure of the brain can be examined at many different levels, spanning many disciplines from low-level biology through psychology and computer science. This thesis focusses on real-time computation of large neural networks using the Izhikevich spiking neuron model. Neural computation has been described as “embarrassingly parallel” as each neuron can be thought of as an independent system, with behaviour described by a mathematical model. However, the real challenge lies in modelling neural communication. While the connectivity of neurons has some parallels with that of electrical systems, its high fan-out results in massive data processing and communication requirements when modelling neural communication, particularly for real-time computations. It is shown that memory bandwidth is the most significant constraint to the scale of real-time neural computation, followed by communication bandwidth, which leads to a decision to implement a neural computation system on a platform based on a network of Field Programmable Gate Arrays (FPGAs), using commercial off- the-shelf components with some custom supporting infrastructure. This brings implementation challenges, particularly lack of on-chip memory, but also many advantages, particularly high-speed transceivers. An algorithm to model neural communication that makes efficient use of memory and communication resources is developed and then used to implement a neural computation system on the multi- FPGA platform. Finding suitable benchmark neural networks for a massively parallel neural computation system proves to be a challenge. A synthetic benchmark that has biologically-plausible fan-out, spike frequency and spike volume is proposed and used to evaluate the system. It is shown to be capable of computing the activity of a network of 256k Izhikevich spiking neurons with a fan-out of 1k in real-time using a network of 4 FPGA boards. This compares favourably with previous work, with the added advantage of scalability to larger neural networks using more FPGAs. It is concluded that communication must be considered as a first-class design constraint when implementing massively parallel neural computation systems.