information aspects of the count in modified fibonacci numerical system

Abstract

The article presents information aspects, laid the basis for the organization of a quick count in the modified Fibonacci numerical system. Analytical expressions are used to describe the basis and the alphabet of this number system. Describes the difference from the classical Fibonacci numerical system and shows how numbers are represented in it. In the modified Fibonacci numerical system can perform over codes Fibonacci conversion with carrying over to the senior categories, which is a conditional arithmetic operation and realizes carrying before the overflow occurs. Expressions are suggested that describe such conversion. Formulated and proved the assertion that if to execute all possible Fibonacci transformation on each clock cycle of direct counting then the resulting code will have no more than two neighboring units. This allows you to organize a quick direct counting without long chains of carrying.