The stability of exponential bidirectional associative memory (eBAM) is proved by using a two-phase approach. The practical capacity of an eBAM considering fault tolerance and fixed dynamic range of MOS transistors is discussed. Other factors are also studied. First, the fault tolerance requirement leads to the discovery of the attraction radius of the basin for each stored pattern pair. Second, the bit-error probability of an eBAM has to be optimally small when a huge number of pattern pairs are encoded in the eBAM. Simulation results are presented to verify the derived theory.