Arithmetic plays a major role in a computer?s performance and efficiency. Building new computing platforms supported by the traditional binary arithmetic and silicon-based technologies to meet the requirements of today?s applications is becoming increasingly more challenging, regardless whether we consider embedded devices or high-performance computers. As a result, a significant amount of research effort has been devoted to the study of nonconventional number systems to investigate more efficient arithmetic circuits and improved computer technologies to facilitate the development of computational units that can meet the requirements of applications in emergent domains. This paper presents an overview of the state of the art in nonconventional computer arithmetic. Several different alternative computing models and emerging technologies are analyzed, such as nanotechnologies, superconductor devices, and biological- and quantum-based computing, and their applications to multiple domains are discussed. A comprehensive approach is followed in a survey of the logarithmic and residue number systems, the hyperdimensional and stochastic computation models, and the arithmetic for quantum- and DNA-based computing systems and techniques for approximate computing. Technologies, processors and systems addressing these nonconventional computer arithmetic systems are also reviewed, taking into consideration some of the most prominent applications, such as deep learning or postquantum cryptography. In the end, some conclusions are drawn, and directions for future research on nonconventional computer arithmetic are discussed.

中文翻译：

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非常规计算机算术电路，系统和应用

算术在计算机的性能和效率中起着重要作用。无论我们是考虑嵌入式设备还是高性能计算机，构建由传统的二进制算术和基于硅的技术支持的新计算平台来满足当今应用程序的需求都变得越来越具有挑战性。结果，大量的研究工作已经投入到非常规数字系统的研究中，以研究更有效的算术电路和改进的计算机技术，以促进能够满足新兴领域应用要求的计算单元的开发。本文概述了非常规计算机算术的最新技术。分析了几种不同的替代计算模型和新兴技术，例如纳米技术，超导体设备以及基于生物和量子的计算，并讨论了它们在多个领域中的应用。在对数和残基数系统，超维和随机计算模型以及基于量子和DNA的计算系统的算术以及近似计算技术的调查中，采用了一种综合方法。还考虑了一些最突出的应用程序，例如深度学习或后量子密码学，对解决这些非常规计算机算术系统的技术，处理器和系统进行了审查。最后得出一些结论，