A Comparison of Linear Sequential Circuits and Arithmetic Sequences

This paper compares the properties of infinitely recurring sequences and terminating sequences generated by arithmetic division with the properties of linear feedback shift registers. The concept of state is defined as equivalent to the remainder or residue in a division process. It is shown that such state graphs have forms identical with those of classes of feedback shift registers. Divisors generating classes of cycles and trees are determined. Sums of such graphs are analyzed. Applications of such arithmetic sequences may be those where feedback shift registers are used. If computers are available, no extra hardware is needed.