On Number Representation

Abstract

Place value numbers, such as the binary or decimal numbers can be represented by the end vertices (leaf or pendant vertices) of rooted symmetrical trees. Numbers that consist of at most a fixed number of digits are represented by vertices that are equidistant from the root vertex and the corresponding number representations do not depend on the distance from the root vertex. In this paper, we introduce number systems that are representable by all vertices of a rooted symmetric tree in such a way that the number representation of each vertex depends on its distance from the root vertex.

arXiv comment26 pages,1 figure, 3 tables v2 was a withdrawal due to a crucial error in Theorem 3.1 and therefore in all subsequent information in v1