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Non-von Neumann computational hardware, based on neuron-inspired, non-linearelements connected via linear, weighted synapses -- so-called neuromorphicsystems -- is a viable computational substrate. Since neuromorphic systems havebeen shown to use less power than CPUs for many applications, they are ofpotential use in autonomous systems such as robots, drones, and satellites, forwhich power resources are at a premium. The power used by neuromorphic systemsis approximately proportional to the number of spiking events produced byneurons on-chip. However, typical information encoding on these chips is in theform of firing rates that unarily encode information. That is, the number ofspikes generated by a neuron is meant to be proportional to an encoded valueused in a computation or algorithm. Unary encoding is less efficient (producesmore spikes) than binary encoding. For this reason, here we presentneuromorphic computational mechanisms for implementing binary two's complementoperations. We use the mechanisms to construct a neuromorphic, binary matrixmultiplication algorithm that may be used as a primitive for lineardifferential equation integration, deep networks, and other standardcalculations. We also construct a random walk circuit and apply it in Brownianmotion simulations. We study how both algorithms scale in circuit size anditeration time.

Binary Operations on Neuromorphic Hardware with Application to Linear Algebraic Operations and Stochastic Equations