Ternary computer

Short description: Computer that uses ternary logic

A ternary computer, also called trinary computer, is one that uses ternary logic (i.e., base 3) instead of the more common binary system (i.e., base 2) in its calculations. Ternary computers use trits, instead of binary bits.

## Contents

* 1 Types of states
* 2 History
* 3 Future applications and research
* 4 Quantum ternary
* 5 Popular culture
* 6 See also
* 7 References
* 8 Further reading
* 9 External links

## Types of states

Ternary computing deals with three discrete states, but the ternary digits themselves can be defined differently:[1]

System  | States

|

Unbalanced ternary  | 0 | 1 | 2
Fractional unbalanced ternary  | 0 | ​1⁄2 | 1
Balanced ternary  | −1 | 0 | 1
Unknown-state logic  | F | ? | T
Ternary-coded binary  | T | F | T

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 unbalanced numbers. These advantages make some calculations more efficient in ternary than binary.[2] Considering that digit signs are mandatory, and nonzero digits are magnitude 1 only, notation that drops the 1s and use only 0 and the + and − signs is more concise than if 1s are included.

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. 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.[3]

## History

> 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.

— Thomas Fowler, letter to Sir George Biddell Airy[4]

One early calculating machine, built entirely from wood by Thomas Fowler in 1840, operated in balanced ternary.[5][6][4]

The first modern, electronic ternary computer, Setun, was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov,[7][8] and it had notable advantages over the binary 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.[7]

In the United States, the ternary computing emulator Ternac working on a binary machine was developed in 1973.[9]: 22 The ternary computer QTC-1 was developed in Canada.[10]

## Future applications and research

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.[2] One possible way this could happen is by combining an optical computer with the ternary logic system.[11] A ternary computer using fiber optics could use dark as 0 and two orthogonal polarizations of light as +1 and −1.[12]

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."[13]

Ternary computing shows promise for implementing fast ternary large language models (LLMs) and potentially other AI applications, in lieu of floating point arithmetic.[14]

With the emergence of carbon nanotube transistors, many research projects have shown interest in designing ternary logic gates using them. Between 2020 and 2024, more than 100 papers about this subject were published on IEEE Xplore.[15]

In 2025, a patent by Huawei proposed a ternary logic gate able to add and subtract ternary inputs. It is introduced as a "ternary logic gate circuit, a computing circuit, a chip, and an electronic device". It uses three transistors with three different voltage level (low, medium and high) to build ternary logic gates.[16]

## Quantum ternary

Ternary quantum computers use qutrits rather than trits. A qutrit is a quantum state that is a complex unit vector in three dimensions, which can be written as |Ψ⟩=α|0⟩+β|1⟩+γ|2⟩ in the bra-ket notation.[17] The labels given to the basis vectors (|0⟩,|1⟩,|2⟩) can be replaced with other labels, for example those given above.

## Popular culture

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".[18]

## See also

* Decimal computer - Computer operating on base-10 numbers
* Flip-flop (electronics)
* Radix economy - Number of digits needed to express a number in a particular base
* Skew binary number system - Non-standard positional numeral system
* Ternary numeral system - Base-3 numeral system
* Ternary signal
* Unconventional computing - Computing by new or unusual methods

## References

1. ↑ Connelly, Jeff (2008). "Ternary Computing Testbed 3-Trit Computer Architecture". California Polytechnic State University of San Luis Obispo. http://xyzzy.freeshell.org/trinary/CPE Report - Ternary Computing Testbed - RC6a.pdf.
2. ↑ 2.0 2.1 Knuth, Donald (1980). The Art of Computer Programming. 2: Seminumerical Algorithms (2nd ed.). Addison-Wesley. pp. 190–192. ISBN 0-201-03822-6. .
3. ↑ "S. Korean researchers develop world's first ternary semiconductor tech". Maeil Business Newspaper. 17 July 2019. https://www.mk.co.kr/news/english/view/2019/07/533039/.
4. ↑ 4.0 4.1 Hayes, Brian (2008-04-01) (in en). Group Theory in the Bedroom, and Other Mathematical Diversions. Farrar, Straus and Giroux. ISBN 978-1-4299-3857-0. https://books.google.com/books?id=1ZkYEFi3DMMC&q=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.&pg=PA196.
5. ↑ McKay, John; Vass, Pamela. "Thomas Fowler". Archived from the original on 31 May 2007. https://web.archive.org/web/20070531221517/http://myweb.tiscali.co.uk/torrington/fowler.htm.
6. ↑ 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.
7. ↑ 7.0 7.1 Nitusov, Alexander. "Nikolay Petrovich Brusentsov". Russian Virtual Computer Museum: Hall of Fame. http://www.computer-museum.ru/english/galglory_en/Brusentsov.htm. Retrieved 25 January 2010.
8. ↑ 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. .
9. ↑ "The development of multiple-valued logic as related to computer science". Computer (IEEE) 7 (9): 20–32. 1974. doi:10.1109/MC.1974.6323304. ISSN 0018-9162.
10. ↑ Cho, Y. H.; Mouftah, H. T. (1988). "A CMOS ternary ROM chip". IEEE. pp. 358–363. doi:10.1109/ISMVL.1988.5195. ISBN 0-8186-0859-5. https://wwwee.ee.bgu.ac.il/~kushnero/ternary/Using CMOS gates/A CMOS ternary ROM chip.pdf.
11. ↑ Jin Yi; He Huacan; Lü Yangtian (2005). "Ternary Optical Computer Architecture". Physica Scripta T118: 98–101. doi:10.1238/Physica.Topical.118a00098. Bibcode: 2005PhST..118...98Y.
12. ↑ Jin, Yi (2003). "Ternary optical computer principle" (in en). Science in China Series F: Information Sciences 46 (2): 145–150. doi:10.1360/03yf9012. ISSN 1009-2757. https://link.springer.com/article/10.1360/03yf9012.
13. ↑ 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). pp. 19–24. doi:10.1109/ISMVL.1998.679270. ISBN 978-0-8186-8371-8.
14. ↑ Ma, Shuming; Wang, Hongyu; Ma, Lingxiao; Wang, Lei; Wang, Wenhui; Huang, Shaohan; Dong, Li; Wang, Ruiping et al. (27 Feb 2024). "The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits". Computation and Language.
15. ↑ "IEEE Xplore Search Results". https://ieeexplore.ieee.org/search/searchresult.jsp?action=search&newsearch=true&matchBoolean=true&queryText=("All Metadata":ternary) AND (("All Metadata":CNFET) OR ("All Metadata":CNTFET)).
16. ↑ ; 黄明强 & 赵广超 et al."Ternary logic gate circuit, computing circuit, chip and electronic device"  patent CN119652311A, issued 2025-03-18
17. ↑ Colin P. Williams (2011). Explorations in Quantum Computing. Springer. pp. 22–23. ISBN 978-1-84628-887-6.
18. ↑ Heinlein, Robert (1982). "Variations on a theme III: Domestic problems". Time Enough for Love. Berkley Books. p. 99. ISBN 978-0-399-11151-8.

## Further reading

* Hunger, Francis (2007) (in en). Eine Recherche über den sowjetischen Ternarcomputer. Institut für Buchkunst Leipzig. ISBN 978-3-932865-48-0.

## External links

* The ternary calculating machine of Thomas Fowler
* Development of ternary computers at Moscow State University
* Tunguska – Ternary Operating System emulator
* Triador: a ternary computer with 600 ternary multiplexers
* 5500FP - modern ternary CPU

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