We treat the one-dimensional Ising model of a binary solution closed in a ring. We analyze the criteria for two-phase behavior of the model system. Bimodality of the distribution function of the atoms over clusters was used as one of the criteria. The effect of the size and dimensionality of the model on the form of the thermodynamic functions is traced. It is shown that in the one-dimensional Ising model of limited size there is a configurational change which can be treated as a smeared phase transition. The results of the present work obtained for a small one-dimensional model agree well with the results for two-dimensional small systems and are analogous to the behavior of three-dimensional systems.