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The work presented in this paper is part of the BAMBI project, which aims at better understanding natural cognition by designing non Von Neumann machines with biologicaly plausible hardware. Probabilistic programming allows artificial systems to better operate with uncertainty, and stochastic arithmetic provides a way to carry out approximate computations with few resources. As such, both are plausible models for natural cognition. Our work on the automatic design of probabilistic machines computing soft inferences with an arithmetic based on stochastic bitstreams allowed us to develop the following compilation toolchain: given a high level description of some general problem (typically to infer some knowledge from a model given some observations), formalized as a Bayesian Program, our toolchain automatically builds a low level description of an electronic circuit computing the corresponding probabilistic inference. This circuit can then be implemented and tested on reconfigurable logic.We designed as a validating example a circuit description of a Bayesian filter solving the problem of Pseudo Noise sequence acquisition in telecommunications.