Researchers in the field of Neuromorphic Engineering are looking at ways to reduce the chip space required to mimic the huge processing capacity of the human brain and to simplify algorithms to train it. Since the recent fabrication of a memristor by the Hewlett Packard Company, there is a possibility to achieve both of these. With their crucial hysteresis properties, memristors can store charge during the training process and respond in a desired manner, electronically mimicking synapse behaviour. This arrangement can reduce chip space and potentially simplify the learning logic. This paper presents HSPICE modeling of an artificial neural network with memristive synapses and training it for ‘AND’ logic. An alternative modification of the memristor model was tried to simplify the learning logic. Results show potential for application in neural circuits.