Arithmetic Operations on Multiple Byte Integers and an Introduction to Multiple Byte Fractions

EasyChair Preprint 5157, version 3

Abstract

Big integers are very essential in many applications. Cryptography is one of these applications. In this study, the objective is to create a multiple byte integer type, with its arithmetic operations defined. The operations are: addition, subtraction, multiplication, division and modular exponentiation are overloaded, to work on this multiple byte integer type.

The creation of the multiple byte integer is done by using doubly linked lists, a well known technique in data structure. The reason is that doubly linked lists enable us to create integer of unlimited size. That is, you do not have to pre-specify the size of the arrays storing these integers.

This is done by dynamically allocating the memory to store the digits constructing the integers.

The operations on these integers are defined using the simple and straight forward techniques, learnt in school.

The results obtained are satisfactory and reliable. The type could be extended to help define multiple byte floating point numbers.

In this work, an improvement has been made to the work of BH Flowers.

Keyphrases: Big Data, Computer Architecture, Numerical Computations, big numbers, data structure

@booklet{EasyChair:5157,
  author    = {Ishraga Mustafa Awad Allam},
  title     = {Arithmetic Operations on Multiple Byte Integers and an Introduction to Multiple Byte Fractions},
  howpublished = {EasyChair Preprint 5157},
  year      = {EasyChair, 2022}}