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A ternary computer (also called trinary computer) is a computer that uses ternary logic (three possible values) instead of the more popular binary system ("Base 2") in its calculations.

Types of statesEdit

Ternary computing deals with three discrete states, but the ternary digits themselves can be defined in different ways, according to Connelly[citation needed]:

  • Unbalanced Trinary – {0,1,2}
  • Fractional Unbalanced Trinary – {0,1/2,1}
  • Balanced Trinary – {-1,0,1}
  • Unknown-State Logic – {F,?,T}
  • Trinary Coded Binary – {T,F,T}


One early calculating machine, built entirely from wood by Thomas Fowler in 1840, operated in balanced ternary.[1][2] The first modern, electronic ternary computer Setun was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov,[3][4] and it had notable advantages over the binary computers which eventually replaced it, such as lower electricity consumption and lower production cost.[3] In 1970 Brusentsov built an enhanced version of the computer, which he called Setun-70.[3] In the USA, the ternary computing emulator Ternac working on a binary machine was developed in 1973.[citation needed]

The ternary computer QTC-1 was developed in Canada.[5]

Balanced ternaryEdit

Ternary computing is commonly implemented in terms of balanced ternary, which uses the three digits −1, 0, and +1. The negative value of any balanced ternary digit 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 decimal numbers. These advantages make some calculations more efficient in ternary than binary.[citation needed] Considering that digit signs are mandatory, and nonzero digits are magnitude 1 only, notation using only zero and signs alone is more concise than when 1's are used.

I often reflect that had the Ternary instead of the denary Notation been adopted in the Infancy of Society, machines something like the present would long ere this have been common, as the transition from mental to mechanical calculation would have been so very obvious and simple.

Unbalanced ternaryEdit

Ternary computing 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.

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 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 in 2017, published on July 15, 2019. [6]

Potential future applicationsEdit

With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However, Donald Knuth argues that they will be brought back into development in the future to take advantage of ternary logic's elegance and efficiency.[7] One possible way this could happen is by combining an optical computer with the ternary logic system.[8] 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.[citation needed]

The Josephson junction 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."[9]

In 2009, a quantum computer was proposed which uses a quantum ternary state, a qutrit, rather than the typical qubit.[citation needed] When the number of basic states of quantum element is d, it is called qudit.[10][clarification needed][11]

Ternary computers in popular cultureEdit

In Robert A. Heinlein's novel Time Enough for Love, 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".[12]

Virtual Adepts in the roleplaying game Mage: The Ascension use ternary computers.

In Howard Tayler's webcomic Schlock Mercenary, 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 than is possible with binary computers.

The Conjoiners, in Alastair Reynolds' Revelation Space series, use ternary logic to program their computers and nanotechnology devices.

Further readingEdit

  • Hunger, Francis (2007). Eine Recherche über den sowjetischen Ternarcomputer [SETUN. An Inquiry into the Soviet Ternary Computer]. Institut für Buchkunst Leipzig. ISBN 978-3-932865-48-0.

See alsoEdit


  1. ^ "Thomas Fowler biography". Archived from the original on 31 May 2007.
  2. ^ a b Glusker, Mark; Hogan, David M.; Vass, Pamela (July–September 2005). "The Ternary Calculating Machine of Thomas Fowler". IEEE Annals of the History of Computing. 27 (3): 4–22. doi:10.1109/mahc.2005.49.
  3. ^ a b c Russian Virtual Computer Museum – Hall of Fame – Nikolay Petrovich Brusentsov, retrieved 2010-01-25.
  4. ^ Trogemann, Georg; Nitussov, Alexander Y.; Ernst, Wolfgang (2001), Computing in Russia: the history of computer devices and information technology revealed, Vieweg+Teubner Verlag, pp. 19, 55, 57, 91, 104–107, ISBN 978-3-528-05757-2.
  5. ^ Y. H. Cho; and H. T. Mouftah. "A CMOS ternary chip".
  6. ^
  7. ^ Knuth, D.E. The Art of Computer Programming – Volume 2: Seminumerical Algorithms, pp. 190–192. Addison-Wesley, 2nd ed., 1980. ISBN 0-201-03822-6.
  8. ^ Jin Yi; He Huacan; Lü Yangtian (2005). "Ternary Optical Computer Architecture". Phys. Scripta. 2005 (98): 98. doi:10.1238/Physica.Topical.118a00098.
  9. ^ Morisue, M.; Endo, J.; Morooka, T.; Shimizu, N.; Sakamoto, M. (1998). "A Josephson ternary memory circuit". Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138): 19–24. doi:10.1109/ISMVL.1998.679270. ISBN 978-0-8186-8371-8.
  10. ^ Brian Wang. "Qudits : multilevel versions of Qubits". 2009.
  11. ^ Brian Wang. "Russia making new type of universal quantum computer with multilevel quantum qudits instead of qubits". 2016.
  12. ^ Heinlein, Robert A. (1982). "Variations on a Theme III: Domestic Problems". Time Enough for Love. Berkley Books. p. 99. ISBN 978-0-399-11151-8.
  13. ^ Ternary "flip-flap-flop"

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