This paper demonstrates the applicability of the constructive stability algorithm of Brayton and Tong in the stability analysis of digital controllers implemented with fixed-point arithmetic. In this paper, we consider a second order digital controller structure. Specifically, we find the allowable parameters that guarantee stability of the controller. Several of the present results are new, while some of the results constitute improvements over existing results. It is emphasized that whereas the existing results are obtained by several diverse methods, the present results are determined by one unified approach.