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Ultra-low energy biologically-inspired neuron and synapse integrated circuits are presented. The synapse includes a spike timing dependent plasticity (STDP) learning rule circuit. These circuits have been designed, fabricated and tested using a 90 nm CMOS process. Experimental measurements demonstrate proper operation. The neuron and the synapse with STDP circuits have an energy consumption of around 0.4 pJ per spike and synaptic operation respectively.