A New Number System Using Alternate Fibonacci Numbers as the Positional Weights with Some Engineering Applications

摘要

Fibonaccian number system (FNS) that uses {0,1} as the digit set with Fibonacci numbers as the positional weights, has many interesting properties which can be exploited for various applications. We propose here a new number system, termed as the Tri-digit Fibonaccian Number System (TFNS), with alternate Fibonacci numbers as the positional weights for the various digits in the representation. We show that TFNS provides asymmetric distribution of the three digits (0,1 and 2) in representing numbers with a pair of consecutive 2's never appearing in a valid codeword. These properties can conveniently be utilized for typical engineering applications, e.g., message encoding for low-energy communication systems and variable length encoding with self-delimiting code.