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Brain-inspired Hyper-dimensional(HD) computing is a novel and efficient computing paradigm. However, highly parallel architectures such as Processing-in-Memory(PIM) are bottle-necked by reduction operations required such as accumulation. To reduce this bottle-neck of HD computing in PIM, we present Stochastic-HD that combines the simplicity of operations in Stochastic Computing (SC) with the complex task solving capabilities of the latest HD computing algorithms. Stochastic-HD leverages deterministic SC, which enables all of HD operations to be done as highly parallel bitwise operations and removes all reduction operations, thus improving the throughput of PIM. To this end, we propose an in-memory hardware design for Stochastic-HD that exploits its high level of parallelism and robustness to approximation. Our hardware uses in-memory bitwise operations along with associative memory-like operations to enable a fast and energy-efficient implementation. With Stochastic-HD, we were able to reach a comparable accuracy with the Baseline-HD. Furthermore, by proposing an integrated Stochastic-HD retraining approach Stochastic-HD is able to reduce the accuracy loss to just 0.3%. We additionally accelerate the retraining process in our hardware design to create an end-to-end accelerator for Stochastic-HD. Finally, we also add support for HD Clustering to Stochastic-HD, which is the first to map the HD Clustering operations to the stochastic domain. As compared to the best PIM design for HD, Stochastic-HD is also 4.4% more accurate and 43.1× more energy-efficient.