Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Utilizing Semi-structured Complex Numbers to Develop the First Division by Zero Calculator

Version 1 : Received: 3 April 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (04:26:06 CEST)

How to cite: Jean Paul, P.; Wahid, S. Utilizing Semi-structured Complex Numbers to Develop the First Division by Zero Calculator. Preprints 2023, 2023040007. https://doi.org/10.20944/preprints202304.0007.v1 Jean Paul, P.; Wahid, S. Utilizing Semi-structured Complex Numbers to Develop the First Division by Zero Calculator. Preprints 2023, 2023040007. https://doi.org/10.20944/preprints202304.0007.v1

## Abstract

Semi-structured complex numbers H was a number set developed to enable division by zero in ordinary algebraic equations. Its utility has been shown in mathematics and engineering. However, very little has been done to show its usefulness in computer science. Consequently, the aim of this paper was to show the utility of semi-structured complex numbers in computer science by developing a division by zero calculator. First two computer programs were written, one for a standard (STD) calculator and the other for a division by zero (DBZ) calculator. The programs were fed 20000 randomly generated arithmetic equations of varying lengths and the space and time complexity associated with processing these equations were measured and compared to determine the efficiency of each calculator. In the process, three major contributions were made: (1) A representation for semi-structured complex numbers that enables it to be easily used by a computer was developed; (2) It was demonstrated that the DBZ calculator outperforms the STD calculator in terms of efficiency; and, (3) It was shown that the number set H reduced the amount of error handling required to run a computer program. These results provide a firm foundation to advance the number set as a useful tool in computer science.

## Keywords

Semi-structured complex numbers; Division by zero; computer science; Calculator; Exception handling

## Subject

Computer Science and Mathematics, Computer Science