Optically bistable devices have an intrinsic two-state memory capability, but practical applications are likely to require the integration of large numbers of bistable elements into arrays of "pixels".[1] The packing density of such pixels will be limited by cross-talk, which may be e.g. thermal, diffusive or diffractive or indeed any combination.[2] The basic requirement of a binary memory is that it have stable states uniquely representing all possible combinations of binary digits. This paper shows how the existence and stability of such states can be established for the case of a linear array with diffusive coupling. Further, an explicit expression is obtained for the minium pixel separation at which full memory function obtains.