Efforts to achieve the long-standing dream of realizing scalable learning algorithms for networks of spiking neurons in silicon have been hampered by (a) the limited scalability of analog neuron circuits; (b) the enormous area overhead of learning circuits, which grows with the number of synapses; and (c) the need to implement all inter-neuron communication via off-chip address-events. In this work, a new architecture is proposed to overcome these challenges by combining innovations in computation, memory, and communication, respectively, to leverage (a) robust digital neuron circuits; (b) novel transposable SRAM arrays that share learning circuits, which grow only with the number of neurons; and (c) crossbar fan-out for efficient on-chip inter-neuron communication. Through tight integration of memory (synapses) and computation (neurons), a highly configurable chip comprising 256 neurons and 64K binary synapses with on-chip learning based on spike-timing dependent plasticity is demonstrated in 45nm SOI-CMOS. Near-threshold, event-driven operation at 0.53V is demonstrated to maximize power efficiency for real-time pattern classification, recognition, and associative memory tasks. Future scalable systems built from the foundation provided by this work will open up possibilities for ubiquitous ultra-dense, ultra-low power brain-like cognitive computers.