THE TRANSFER AND BORROWING METHODS IN FAST FIBONACCI COUNTERS

Abstract

This article describes the approach to the organization of carry-over with the account in the modified Fibonacci numerical system. This approach is based on the fact that on each count cycle, along with the addition of a unit to the low order depending on the direction of the account, one of the Fibonacci transformation types (F-transformation ) of the counter code is executed. Using FL- and FR-transformation allows you to carry out the carrying and borrowing even before there is an overflow in the lower or loss in the higher order bits. This makes it possible to avoid situations in which the carrying or borrowing is extended more than three orders in a single clock cycle. The article describes the modified Fibonacci numerical system, provides analytical expressions for describing the basis and the alphabet, and shows how the numbers are represented in it. Analytical expressions describing FL and FR transformations are given. An assertion is made that when all possible Fibonacci transformations are performed on each circle of count, the resulting code will have no more than two neighboring units. This allows you to organize a quick count due to the short transfer and borrowing time.