Identifying minimal shift counters: A search technique
Abstract
A minimal modulom nstage shift counter is defined as a shift counter with a feedback function of the form Y(sub 1) = y(sub n) direct sum P(sub 1)(y(sub 1), y(sub 2), ..., y(sub n  1))direct sum ...direct sum P(sub k)(y(sub 1), y(sub 2), ..., y(sub n  1)), where y(sub n) is either y(sub n) or y''(sub n) and P(sub i)(y(sub 1), y(sub 2), ..., y(sub n  1)) is a product of literals of state variables. The feedback function is selected from the set of 2(exp 2n  1) functions that can be represented in this form so as to minimize the number of product terms, the number of literals of a product term, and the total number of literals, in this order. Due to the shift register properties introduced in this brief contribution, it is possible to identify minimal shift counters using a search technique. Minimal shift counters with up to 14 stages have been identified. Except for very small moduli (m less than 2n), minimal shift counters can be operated at higher frequencies and require a smaller area than shift counters designed using other methods.
 Publication:

IEEE Transactions on Computers
 Pub Date:
 May 1994
 Bibcode:
 1994ITCmp..43..633T
 Keywords:

 Identifying;
 Integrated Circuits;
 Logic Design;
 Shift Registers;
 Counters;
 Feedback;
 Functions (Mathematics);
 Electronics and Electrical Engineering