Abstract
While silicon-based electronic computing systems have been successful in exploiting binary arithmetic, the positional nature of binary representation itself imposes the need to handle both carrying generation and carrying propagation. The current computers are thus limited in terms of the extent of parallelism possible and require excessive power. This article explores the possibilities of using two specific unconventional number representations Sousa, (2021), namely, logarithmic number systems (LNS) and residue number system (RNS), which offer parallelism while increasing energy efficiency also. Both LNS and RNS arithmetic take all dimensions of the system into account, which include not only computer arithmetic theory but also technological advances and emergent applications. Both have their own individual strong suits as well as limitations. LNS provides for extremely fast multiplication and division; while for addition and subtraction, it requires the use of look-up tables. RNS, in comparison, is used across a variety of domains including nanophotonic computers, DNA-based computing, integrated photonics, and cryptography. Different technologies have different uses and operate differently internally, which is where unconventional number systems can come in and specialize each piece of technology.