Counting with Nonlinear Binary Feedback Shift Registers

This paper discusses methods of designing binary nonlinear feedback shift registers with cycles of specified length. First, the cycle structures of the simplest feedback functions, e.g., the circulating shift function, are considered. It is then shown how such structures may be modified, either by joining two suitable cycles into one or by the reverse process of splitting a cycle into two. By properly applying these two methods, namely cycle joining and cycle splitting, a wide range of binary shift registers having relatively simple feedback logic is easily designed.