The Time Machine (TM) is a spike-based computation architecture that represents synaptic weights in time. This choice of weight representation allows the use of virtual synapses, providing an excellent tradeoff in terms of flexibility, arbitrary weight connections and hardware usage compared to dedicated synapse architectures. The TM supports an arbitrary number of synapses and is limited only by the number of simultaneously active synapses to each neuron. SpikeSim, a behavioral hardware simulator for the architecture, is described along with example algorithms for edge detection and objection recognition. The TM can implement traditional spike-based processing as well as recently developed time mode operations where step functions serve as the input and output of each neuron block. A custom hybrid digital/analog implementation and a fully digital realization of the TM are discussed. An analog chip with 32 neurons, 1024 synapses and an address event representation (AER) block has been fabricated in 0.5 μm technology. A fully digital field-programmable gate array (FPGA)-based implementation of the architecture has 6,144 neurons and 100,352 simultaneously active synapses. Both implementations utilize a digital controller for routing spikes that can process up to 34 million synapses per second.