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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. The authors' work on the automatic design of probabilistic machines computing soft inferences, with an arithmetic based on stochastic bitstreams, allowed to develop the following compilation toolchain: given a high-level description of some general problem, formalized as a Bayesian Program, the 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. This paper describes two circuits as validating examples. The first one implements a Bayesian filter solving the problem of Pseudo Noise sequence acquisition in telecommunications. The second one implements decision making in a sensorimotor system: it allows a simple robot to avoid obstacles using Bayesian sensor fusion.