Review of Basic Classes of Dividers Based on Division Algorithm

Abstract

The electronics world is very well described in two distinct but dependent interdisciplinary areas, namely hardware and software. Arithmetic operations are very vital building blocks of an electronic system. An algorithm is a systematic arrangement that helps develop a sophisticated electronic system, including hardware and software aspects. Addition, subtraction, multiplication, and division are critical elements of arithmetic implementation in the electronic system, but fewer efforts have been made to implement division than other arithmetic operations, even though the number of transistors on a chip is increasing beyond the Moore's law prediction. It is quite complicated to implement arithmetical operations; here, a sophisticated algorithm is essential to successful implementation. Technological upgrades are leading to a new paradigm of applications, where the performance of a division circuit or block is a vital and critical feature of a successful system. The lexicon of algorithms used in the implementation of the division operation in electronics systems is discussed in detail in the present article, which indicates the mathematical formulation, criticality, conversion pattern, hardware requirements, and logic used for conversion. The current report describes the broad classification of dividers into basic classes named digit recurrence, high radix, functional iteration, estimation, a look-up table, and variable latency. It also illustrates that, in practical implementation, many algorithms have been developed that combine one or many classes and are implemented with different hardware architectures. The study indicated the possibility of improving the presently available algorithms or creating a new algorithm to enhance practical implementation.