Neuromorphic computing is a non-von Neumann computer architecture for the post Moore’s law era of computing. Since a main focus of the post Moore’s law era is energy-efficient computing with fewer resources and less area, neuromorphic computing contributes effectively in this research. In this paper we present a memristive neuromorphic system for improved power and area efficiency. Our particular mixed-signal approach implements neural networks with spiking events in a synchronous way. Moreover, the use of nano-scale memristive devices saves both area and power in the system. We also provide device-level considerations that make the system more energy-efficient. The proposed system additionally includes synchronous digital long term plasticity (DLTP), an online learning methodology that helps the system train the neural networks during the operation phase and improves the efficiency in learning considering the power consumption and area overhead.