for inference is called DISCRETE-SAMPLE, which generates draws from a discrete-output probability distribution whose weights are specified on its input. For example, in Gibbs sampling, this distribution is the conditional probability of one variable given the current value of all other variables that directly depend on it. One implementation of this operation is shown in Figure 3A; each stochastic transition circuit from Figure 2 could be implemented by one such circuit, with multiplexers to select log-probability values based on the neighbors of each random variable. Because only the ratios of the raw probabilities matter, and the probabilities themselves naturally vary on a log scale, extremely low precision representations can still provide accurate results. High entropy (i.e. nearly uniform) distributions are resilient to truncation because their values are nearly equal to begin with, differing only slightly in terms of their low-order bits. Low entropy (i.e. nearly deterministic) distributions are resilient because truncation is unlikely to change which outcomes have nonzero probability. Figure 3B quantifies this low-precision property, showing the relative entropy (a canonical information theoretic measure of the difference between two distributions) between the output distributions of low precision implementations of the circuit from Figure 3A and an accurate floating-point implementation. 