CMOS-memristor circuit is constructed to behave as a trainable artificial synapse for neuromorphic hardware systems. The invention relies on the memristance of a memristor at the input side of the device to act as a reconfigurable weight that is adjusted to realize a desired function. The invention relies on charge sharing at the output to enable the summation of signals from multiple synapses at the input node of a neuron circuit, implemented using a CMOS amplifier circuit. The combination of several memristive synapses and a neuron circuit constitute a neuromorphic circuit capable of learning and implementing a multitude of possible functionalities.