  There is evidence that biological synapses have only a fixed number of
discrete weight states. Memory storage with such synapses behaves quite
differently from synapses with unbounded, continuous weights as old memories
are automatically overwritten by new memories. We calculate the storage
capacity of discrete, bounded synapses in terms of Shannon information. For
optimal learning rules, we investigate how information storage depends on the
number of synapses, the number of synaptic states and the coding sparseness.
