it's interesting, NN degrade at about 6bit, and that's mostly because the transfer function become stable and the training gets stuck more often in local minimums.
we built a training methodology in two step, first you trained them in 16bit precision, finding the absolute minimum, then retrain them with 6bit precision, and the NN basically learned to cope with the precision loss on its own.
funny part is, the less bit you have, the more robust the network became, because error correcting became a normal part of its transfer function.
we couldn't make the network solution converge on 4bit however. we tried using different transfer function, but then ran out of time before getting meaningful results (Each function needs it's own back propagation adjustment and things like that take time, I'm not a mathematician :D)