The use of online arithmetic was often proposed for hardware implementations of complex digital-signal processing (DSP) algorithms. However, several important issues in the design process of such algorithms using online arithmetic are rarely discussed in the literature. This paper presents these issues and provides a methodology to analyze the behavior of networks of online arithmetic modules performing serial computation over fixed-point numbers. The methodology is presented, applied in several examples, and finally used to design an efficient field programmable gate arrays implementation of the Levinson-Durbin algorithm in an application of the Yule-Walker power spectrum estimation. The methodology can be applied to other algorithms as well and it simplifies the task of designing and verifying a network of online modules. The experimental results show the advantages of online arithmetic in the design of complex DSP algorithms.