A class of arithmetic burst-error-correcting codes for the fibonacci computer
Viet-Dung Hoang · 1979
For computers whose main components are on a single chip, as microprocessors, the errors, instead of being randomly scattered, are more apt to be localized in the form of bursts in the chip. Burst-errors, also known as non-uniform errors, or errors to consecutive digits, are becoming an important and practical problem in these new computers and their resulting arithmetic coding theory. With technology moving toward making integrated circuit (I.C.) chips of groups of bits (the bytes) the building block units, codes are useful indeed. In order to produce better codes, it is felt that not only the present day hardware needs to be improved but also a better number base is needed to be developed in which the computer does its calculation, as well as a superior coding theory. The Fibonacci numbers are proposed as a new number base system for computers, which could lead to more error-free operations. The motivation to use these numbers comes from a property of considerable importance: the existence of a non-adjacent-form Fibonacci representation of integers. This study is divided into four major parts: (1) section one formulates the Fibonacci number system. (2) section two shows the implementation of the Fibonacci Computer's Arithmetic Unit using existing binary logic. (3) section three studies the two basic Fibonacci arithmetic codes: the Fibonacci AN codes and the Fibonacci biresidue codes. (4) section four gives the theory of the Fibonacci AN codes. It is the intention of this study to demonstrate that the Fibonacci computer's architecture produces more superior arithmetic codes than their binary system's counterparts. This burst-error-correcting property, not seen in the binary system, makes Fibonacci computer theoretically interesting as well as practically important.