We introduce a novel, greatly simplified classifier for binarized data. The model contains a sparse, "digital" hidden layer of Parity interactions, followed by a sigmoidal output node. We propose priors for the cases: a) input space obeys a metrics; b) inputs encode discrete attributes. Stochastic search for the hidden layer allows capacity and smoothness of the approximation to be controlled by two complexity parameters. Aggregation of classifiers improves predictions. Interpretable results are obtained in some cases. We point out the impact of our model on real-time systems, suitability for sampling and aggregation techniques, and possible contributions to nonstandard learning devices.