Embodiments of the invention relate to a time-division multiplexed neurosynaptic module with implicit memory addressing for implementing a universal substrate of adaptation. One embodiment comprises a neurosynaptic device including a memory device that maintains neuron attributes for multiple neurons. The module further includes multiple bit maps that maintain incoming firing events for different periods of delay and a multi-way processor. The processor includes a memory array that maintains a plurality of synaptic weights. The processor integrates incoming firing events in a time-division multiplexing manner. Incoming firing events are integrated based on the neuron attributes and the synaptic weights maintained.