Compared to conventional processors, stochastic computing architectures have strong potential to speed up computation time and to reduce power consumption. We present such an architecture, called Bayesian Machine (BM), dedicated to solving Bayesian inference problems. Given a set of noisy signals provided by low-level sensors, a BM estimates the posterior probability distribution of an unknown target information. In the present study, a BM is used to solve a sound source localization (SSL) problem: the BM computes the probability distribution of the position of a sound source given acoustic signals captured by a set of microphones. Assuming free field wave propagation (no reverberations), we express the SSL problem as the maximization of a likelihood function fed with audio features provided by the time-frequency (TF) analysis of the captured audio waves. The proposed BM uses bitwise parallel sampling to fuse the resulting multi-channel information. As the number of channels to fuse is large, the standard BM architecture encounters the so-called " time dilution problem " (long delays are necessary to obtain valid samples). We tackle this problem by using max-normalization of the distributions combined with a periodic re-sampling of the bit streams after processing a reasonably small subset of evidences. Finally, we compare the localization performance of the proposed machine with the results obtained using a standard version of the machine. The re-sampling leads to an impressive acceleration factor of 10³ in the computation.