Spiking neural networks (SNNs) are being explored in an attempt to mimic brain's capability to learn and recognize at low power. Crossbar architecture with highly scalable Resistive RAM or RRAM array serving as synaptic weights and neuronal drivers in the periphery is an attractive option for SNN. Recognition (akin to reading the synaptic weight) requires small amplitude bias applied across the RRAM to minimize conductance change. Learning (akin to writing or updating the synaptic weight) requires large amplitude bias pulses to produce a conductance change. The contradictory bias amplitude requirement to perform reading and writing simultaneously and asynchronously, akin to biology, is a major challenge. Solutions suggested in the literature rely on time-division-multiplexing of read and write operations based on clocks, or approximations ignoring the reading when coincidental with writing. In this work, we overcome this challenge and present a clock-less approach wherein reading and writing are performed in different frequency domains. This enables learning and recognition simultaneously on an SNN. We validate our scheme in SPICE circuit simulator by translating a two-layered feed-forward Iris classifying SNN to demonstrate software-equivalent performance. The system performance is not adversely affected by a voltage dependence of conductance in realistic RRAMs, despite departing from linearity. Overall, our approach enables direct implementation of biological SNN algorithms in hardware.