Efficiency Analysis and Optimization Techniques for Base Conversion Algorithms in Computational Systems

Abstract

The performance of base conversion methods varies greatly across several techniques, and this is important for computer-based systems. This research paper therefore examines the efficiency of three base conversion methods namely; Successive Multiplication Method, Positional Notation Method, and Horner’s Method. Their execution times are evaluated for binary, octal, decimal, and hexadecimal bases with input sizes that range from 1000 to 10,000 digits. Empirical results show that on average Horner’s Method outperforms other methods by having about 40% better execution times and up to 30% more uniformity than Positional Notation Method based upon repeated application of decimal points. Specifically speaking, for hexadecimal conversions, it took on average 0.009 seconds for Horner’s method as against 0.460 seconds for Positional Notation and another 0.009 seconds Successive Multiplication method. These observations indicate that Horner’s method is the most efficient in terms of time taken during a base conversion process as well as its consistency when compared to other techniques used in performing the same task throughout different bases such as decimal point addition repeatedly considered in positional notation numeral system. Notably, Horner’s Method completed a hexadecimal conversion at an average rate of one every nine milliseconds on the other hand the Positional Notation Approach finished one conversion per second while the Successive Multiplication Technique performed at best zero conversions within a given unit of time. It accomplishes these tasks much faster than previous approaches because it does not require multiplication steps or many intermediate calculations before obtaining answers like in Problem I; instead, only a few additions per digit are required which can be done more quickly using modern hardware such as programmable logic arrays (PLAs) according to writer P1 - R3 or even printed circuit boards (PCBs).