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During the past few decades, a significant amount of research effort has been dedicated toward developing skin-inspired sensors for real-time human motion monitoring and next-generation robotic devices. Although several flexible and wearable sensors have been developed in the past, the need of the hour is developing accurate, reliable, sophisticated, facile yet inexpensive flexible sensors coupled with neuromorphic systems or spiking neural networks to encode tactile information without the need for complex digital architectures, thus achieving true skin-like sensing with limited resources. In this work, we propose an approach entailing carbon nanofiber-polydimethylsiloxane composite-based piezoresistive sensors, coupled with spiking neural networks, to mimic skin-like sensing. The strain and pressure sensors have been combined with appropriately designed neural networks to encode analog voltages to spikes to recreate bioinspired tactile sensing and proprioception. To further validate the proprioceptive capability of the system, a gesture tracking smart glove, combined with a spiking neural network, was demonstrated. Wearable and flexible sensors with accompanying neural networks such as the ones proposed in this work will pave the way for a future generation of skin-mimetic sensors for advanced prosthetic devices, apparel integrable smart sensors for human motion monitoring, and human-machine interfaces.