On-line fundamental arithmetic algorithms for three-dimensional vector system

Abstract

This research is to introduce a novel three-dimensional vector representation system. The proposed system composes of an integer base and a finite set of signed-vector-digit. The research is also focused on an on-line computation mode combining with a pipelining concept. An important characteristic for an on-line system is also studied, that is the on-line delay, the smallest integer which is the number of digits of the inputs used for producing the first digit of the output. In order to do this, the vector representation system should be a redundant system which means any vector can have more than one finite representation. The concept of signed digit number system is applied to this work. Using the new representation, some fundamental arithmetic operations for three-dimensional vector such as addition, subtraction, and multiplication (cross product) are shown to be realized, similar to the classical number system.