IEEE Circuits and Systems Magazine - Q1 2021 - 7

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.

I. Introduction
he demise of Moore's Law and the waning of
Dennard scaling, which respectively stated
that the number of tra nsistors on silicon
chips would double every two years and that this increase in the transistor density is not achieved at constant power consumption [1], mark the end of an era in
which the computational capacity growth was mainly
based on the downscaling of silicon-based technology.
At the same time, the demand for data processing is
higher than ever before as a result of the more than
2.5 quintillion bytes that are created on a daily basis
[2]. This number continues to grow exponentially, and
therefore, ingenious solutions must be developed to
address the limitations of traditional computational
systems. These innovative solutions must include developments not only at the technological level but also
at the arithmetic, architectural and algorithmic levels
of computing.
Although binary arithmetic has been successfully
used to design silicon-based computing systems, the
positional nature of this representation imposes the
processing of carry chains, which precludes the exploitation of parallelism at the most basic levels and leads
to high power consumption. Hence, the research on unconventional number systems is of the utmost interest
to explore parallelism and take advantage of the characteristics of emerging technologies to improve both
the performance and the energy efficiency of computational systems. Moreover, by avoiding the dependencies of binary systems, nonconventional number systems can also support the design of reliable computing
systems using the newest available technologies, such
as nanotechnologies.

A. Motivation
The Complementary Metal-Oxide Semiconductor (CMOS)
transistor was invented over fifty years ago and has
played a key role in the development of modern electronic devices and all that it has enabled. The CMOS transistor has evolved into nanodevices, with characteristic
dimensions less than 100 nm. The downscaling of the
gate length has become one of the biggest challenges
hindering progression in each new generation of CMOS
transistors and integrated circuits. New device architectures and materials have been proposed to address
this challenge, namely, the Fin Field-Effect transistor
(FinFET) multigate devices [5]. This type of nonplanar
transistor became the dominant gate design from the
14 nm/10 nm generations, used in a broad range of applications, ranging from consumer applications to embedded systems and high-performance computing [6].
Fig. 1 plots the cost, speed, size, and energy per operation relationship for the CMOS and other emerging
nanotechnologies; all the scales are logarithmic, covering many orders of magnitude. Examples of these technologies include superconducting electronics, molecular
electronics, resonant tunneling devices, quantum cellular automata, and optical switches.
Superconducting digital logic circuits use SingleFlux Quantum (SFQ), also known as magnetic flux
quanta, to encode and process data. An Rapid Single
Flux Quantum (RSFQ) device is a superconducting ring
with a Josephson junction that opens and closes to
admit or expel a flux quanta. The Adiabatic QuantumFlux-Parametron (AQFP), another SFQ-based device
not represented in the figure with characteristics that
are analyzed later in this survey, drastically reduces
the energy dissipation by using Alternating Current
(AC) bias/excitation currents for both the clock signal
and power supply. This is high-speed nanotechnology
that offers low-power dissipation and scalability. However, its main drawbacks include the need for expensive cooling technologies and improved techniques
in manufacturing the elements. Molecular electronics
use a single molecule as the switch. The configuration
of the molecule determines its state, thereby " switching " on or off the current flow through the molecule.
While conceptually appealing, the molecular process
exhibits poor self-assembly techniques and low reproducibility. In Quantum Cellular Automata (QCA), cells
are switched on and off by moving the position of the
electrons from one cell to another. Classical physics
does not apply to these technologies, which support,

Leonel Sousa is with the Department of Electrical and Computer Engineering, INESC-ID, Instituto Superior Técnico, Universidade de Lisboa; Address:
Rua Alves Redol, 9, 1000-029 Lisboa, PORTUGAL; e-mail: las@inesc-id.pt.
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