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Based on the tight-binding model of the single electron, the one-dimensional Anderson model with random binary distributed on-site energies is studied using the transfer-matrix approach. We calculate numerically the localization length, the density of the electronic states and the Lyapunov exponent. The results show that the localization length strongly depends on energies and is affected by disordered degrees to some extent. With finite size systems, the localization length presents obvious effect on the impurity concentration. While in the dilute limit there exist extended states, increasing the impurity concentration beyond a critical value destroys these extended states and the localization length over the entire energy range becomes smaller than the system size. By studying the scaling relation, we find that the localized states are stable in the thermodynamic limit. Transforming the random matrix product into a conformal map, we introduce the Lyapunov exponent, which is finite within the entire band in our model. Starting from the Lyapunov exponent, the localization length and the density of states may also be obtained. [ABSTRACT FROM AUTHOR]