  Recent work has explored binary waveguide arrays in the long-wavelength,
near-continuum limit, here we examine the opposite limit, namely the vicinity
of the so-called anti-continuum limit. We provide a systematic discussion of
states involving one, two and three excited waveguides, and provide comparisons
that illustrate how the stability of these states differ from the monoatomic
limit of a single type of waveguide. We do so by developing a general theory
which systematically tracks down the key eigenvalues of the linearized system.
When we find the states to be unstable, we explore their dynamical evolution
through direct numerical simulations. The latter typically illustrate, for the
parameter values considered herein, the persistence of localized dynamics and
the emergence for the duration of our simulations of robust quasi-periodic
states for two excited sites. As the number of excited nodes increase, the
unstable dynamics feature less regular oscillations of the solution's
amplitude.
