A ternary computer, also called trinary computer, is one that uses
ternary logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate ...
(i.e.,
base 3
A ternary numeral system (also called base 3 or trinary) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log2 3 (about 1.58496) bits of information.
Although ''ternary'' m ...
) instead of the more common
binary system
A binary system is a system of two astronomical bodies which are close enough that their gravitational attraction causes them to orbit each other around a barycenter ''(also see animated examples)''. More restrictive definitions require that th ...
(i.e.,
base 2) in its calculations. This means it uses trits (instead of
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s, as most computers do).
Types of states
Ternary computing deals with three discrete states, but the ternary digits themselves can be defined differently:
Ternary quantum computers use
qutrit
A qutrit (or quantum trit) is a unit of quantum information that is realized by a 3-level quantum system, that may be in a superposition of three mutually orthogonal quantum states.
The qutrit is analogous to the classical radix-3 trit, just as ...
s rather than trits. A qutrit is a
quantum state
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in ...
that is a
complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat").
The term ''direction vecto ...
in three dimensions, which can be written as
in the
bra-ket notation. The labels given to the
basis vector
In mathematics, a set of vectors in a vector space is called a basis if every element of may be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as components ...
s (
) can be replaced with other labels, for example those given above.
History
One early calculating machine, built entirely from wood by Thomas Fowler in 1840, operated in balanced ternary.
The first modern, electronic ternary computer,
Setun
Setun (russian: Сетунь) was a computer developed in 1958 at Moscow State University. It was built under the leadership of Sergei Sobolev and Nikolay Brusentsov. It was the most modern ternary computer, using the balanced ternary numeral sys ...
, was built in 1958 in the Soviet Union at the
Moscow State University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
by
Nikolay Brusentsov
Nikolay Petrovich Brusentsov (russian: Никола́й Петро́вич Брусенцо́в; 7 February 1925 in Kamenskoe, Ukrainian SSR – 4 December 2014) was a computer scientist, most famous for having built a (balanced) ternary computer ...
,
and it had notable advantages over the
binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that ta ...
computers that eventually replaced it, such as lower electricity consumption and lower production cost.
In 1970 Brusentsov built an enhanced version of the computer, which he called Setun-70.
In the United States, the ternary computing emulator
Ternac TERNAC is an emulation written in FORTRAN of a ternary computer on another binary machine, a Burroughs B1700. It was implemented in 1973 at State University of New York, Buffalo (SUNY Buffalo). The implementation provided both fixed-point and flo ...
working on a binary machine was developed in 1973.
The ternary computer QTC-1 was developed in Canada.
Balanced ternary
Ternary computing is commonly implemented in terms of
balanced ternary
Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanc ...
, which uses the three digits −1, 0, and +1. The negative value of any balanced
ternary digit
A ternary numeral system (also called base 3 or trinary) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log2 3 (about 1.58496) bits of information.
Although ''ternary'' mo ...
can be obtained by replacing every + with a − and vice versa. It is easy to subtract a number by inverting the + and − digits and then using normal addition. Balanced ternary can express negative values as easily as positive ones, without the need for a leading negative sign as with unbalanced numbers. These advantages make some calculations more efficient in ternary than binary.
Considering that digit signs are mandatory, and nonzero digits are magnitude 1 only, notation that drops the '1's and use only zero and the + − signs is more concise than if 1's are included.
Unbalanced ternary
Ternary computing can be implemented in terms of unbalanced ternary, which uses the three digits 0, 1, 2. The original 0 and 1 are explained as an ordinary
Binary computer, but instead uses 2 as
leakage current
In electronics, leakage is the gradual transfer of electrical energy across a boundary normally viewed as insulating, such as the spontaneous discharge of a charged capacitor, magnetic coupling of a transformer with other components, or flow of cu ...
.
The world's first unbalanced ternary semiconductor design on a large wafer was implemented by the research team led by Kim Kyung-rok at
Ulsan National Institute of Science and Technology
Ulsan National Institute of Science and Technology, simply referred to as UNIST (), is one of the four public universities in South Korea which are dedicated to research in science and technology, along with KAIST, GIST, and DGIST. UNIST was ...
in South Korea, which will help development of low power and high computing microchips in the future. This research theme was selected as one of the future projects funded by
Samsung
The Samsung Group (or simply Samsung) ( ko, 삼성 ) is a South Korean multinational manufacturing conglomerate headquartered in Samsung Town, Seoul, South Korea. It comprises numerous affiliated businesses, most of them united under the ...
in 2017, published on July 15, 2019.
Potential future applications
With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However,
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...
argues that they will be brought back into development in the future to take advantage of ternary logic's elegance and efficiency.
[.] One possible way this could happen is by combining an
optical computer
Optical computing or photonic computing uses light waves produced by lasers or incoherent sources for data processing, data storage or data communication for computing. For decades, photons have shown promise to enable a higher bandwidth than the ...
with the
ternary logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminate ...
system. A ternary computer using fiber optics could use dark as 0 and two orthogonal polarizations of light as +1 and −1. IBM also reports infrequently on ternary computing topics (in its papers), but it is not actively engaged in it.
The
Josephson junction
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
has been proposed as a balanced ternary memory cell, using circulating superconducting currents, either clockwise, counterclockwise, or off. "The advantages of the proposed memory circuit are capability of high speed computation, low power consumption and very simple construction with fewer elements due to the ternary operation."
Ternary computers in popular culture
In
Robert A. Heinlein
Robert Anson Heinlein (; July 7, 1907 – May 8, 1988) was an American science fiction author, aeronautical engineer, and naval officer. Sometimes called the "dean of science fiction writers", he was among the first to emphasize scientific accu ...
's novel ''
Time Enough for Love
''Time Enough for Love'' is a science fiction novel by American writer Robert A. Heinlein, first published in 1973. The work was nominated for the Nebula Award for Best Novel in 1973 and both the Hugo and Locus Awards in 1974.
Plot
The book cov ...
'', the sapient computers of Secundus, the planet on which part of the framing story is set, including Minerva, use an unbalanced ternary system. Minerva, in reporting a calculation result, says "three hundred forty one thousand six hundred forty... the original ternary readout is unit pair pair comma unit nil nil comma unit pair pair comma unit nil nil point nil".
Virtual Adepts in the roleplaying game ''
Mage: The Ascension
''Mage: The Ascension'' is a role-playing game based in the World of Darkness, and was published by White Wolf Game Studio in 1993. The characters portrayed in the game are referred to as mages, and are capable of feats of magic. Magic in ''Ma ...
'' use ternary computers.
In
Howard Tayler
Howard V. Tayler (born February 29, 1968 in Florida) is the creator of the webcomic ''Schlock Mercenary''. He worked as a volunteer missionary for the LDS Church, then graduated from Brigham Young University. Using his degree in music compositi ...
's webcomic ''
Schlock Mercenary
''Schlock Mercenary'' is a comedic webcomic written and drawn by Howard Tayler. It follows the tribulations of a star-travelling mercenary company in a satiric, mildly dystopian 31st-century space opera setting. After its debut on June 12, 2000 ...
'', every modern computer is a ternary computer. AIs use the extra digit as "maybe" in boolean (true/false) operations, thus having a much more intimate understanding of
fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely ...
than is possible with binary computers.
The Conjoiners, in
Alastair Reynolds
Alastair Preston Reynolds (born 13 March 1966) is a Welsh science fiction author. He specialises in hard science fiction and space opera. He spent his early years in Cornwall, moved back to Wales before going to Newcastle University, where he s ...
' ''
Revelation Space
''Revelation Space'' is a 2000 science fiction novel by Welsh author Alastair Reynolds. It was the first novel (but not first published work of fiction) set in Reynolds's eponymous universe. The novel reflects Reynolds's professional background ...
'' series, use ternary logic to program their computers and nanotechnology devices.
In
Stanisław Lem
Stanisław Herman Lem (; 12 September 1921 – 27 March 2006) was a Polish writer of science fiction and essays on various subjects, including philosophy, futurology, and literary criticism. Many of his science fiction stories are of satirical ...
's short story "The Hunt", the robot hunted by the protagonist is called Setaur, Self-programming Electronic Ternary Automaton Racemic.
Tasen and Komato aliens, in the computer game ''
Iji
''Iji'' is a freeware 2008 video game featuring platform and shooting elements, developed by Daniel Remar using Game Maker over a period of four years. In the game, the player controls Iji Kataiser, a young woman enhanced with nanotechnology, ...
'', use ternary logic to program their nanotechnology.
See also
*
Radix economy
The radix economy of a number in a particular base (or radix) is the number of digits needed to express it in that base, multiplied by the base (the number of possible values each digit could have). This is one of various proposals that have been ...
*
Ternary numeral system
A ternary numeral system (also called base 3 or trinary) has three as its base. Analogous to a bit, a ternary digit is a trit (trinary digit). One trit is equivalent to log2 3 (about 1.58496) bits of information.
Although ''ternary'' mo ...
*
Skew binary number system
Skew may refer to:
In mathematics
* Skew lines, neither parallel nor intersecting.
* Skew normal distribution, a probability distribution
* Skew field or division ring
* Skew-Hermitian matrix
* Skew lattice
* Skew polygon, whose vertices do not l ...
*
Ternary signal In telecommunication, a ternary signal is a signal that can assume, at any given instant, one of three states or significant conditions, such as power level, phase position, pulse duration, or frequency.
Examples of ternary signals are (a) a puls ...
*
Flip-flap-flop
*
Ternary SRAM
*
Decimal computer
Decimal computers are computers which can represent numbers and addresses in decimal as well as providing instructions to operate on those numbers and addresses directly in decimal, without conversion to a pure binary representation. Some also h ...
References
Further reading
*
External links
The ternary calculating machine of Thomas Fowler3niti – Collaboration for Open Ternary Computer Development* {{cite web
, url=http://roluan.com
, title=ROLUAN – Ternary ecosystem startup. Ternary software and hardware. Open source.
, last=
, first=
, date=
, website=
, publisher=
, access-date=
, quote=
, archive-url=https://web.archive.org/web/20180322060200/http://roluan.com/
, archive-date=2018-03-22
, url-status=dead
SBTCVM – Open-source balanced ternary emulation project
Triador: a ternary computer with 600 ternary multiplexers
Classes of computers
Russian inventions
Soviet inventions