Editing Setun (section)

== ternary compared to binary ==
[[Balanced ternary|Balanced ternary system]]<nowiki/>s and ternary computers are not unprecedented in history. Thomas Fowler built a mechanical computer in 1840 using balanced ternary system.<ref name="tf1">{{cite web |last1=McKay |first1=John |last2=Vass |first2=Pamela |title=Thomas Fowler |url=http://myweb.tiscali.co.uk/torrington/fowler.htm |url-status=dead |archiveurl=https://web.archive.org/web/20070531221517/http://myweb.tiscali.co.uk/torrington/fowler.htm |archivedate=31 May 2007}}</ref> The balanced ternary representation of numbers and its related arithmetics was applied in number theory back to [[Leonhard Euler]]<ref>{{cite journal |last=Andrews |first=George E. |year=2007 |title=Euler's "De Partitio numerorum" |journal=Bulletin of the American Mathematical Society |series=New Series |volume=44 |issue=4 |pages=561–573 |doi=10.1090/S0273-0979-07-01180-9 |mr=2338365 |doi-access=free}}</ref> and was briefly discussed by [[Claude Shannon]] in his paper ''a symmetric notation of numbers'' published in 1950.<ref>{{Cite journal |last=Shannon |first=C. E. |date=February 1950 |title=A Symmetrical Notation for Numbers |url=https://doi.org/10.1080/00029890.1950.11999490 |journal=The American Mathematical Monthly |volume=57 |issue=2 |pages=90–93 |doi=10.1080/00029890.1950.11999490 |issn=0002-9890}}</ref>

Despite the ternary design never become massively produced, there have been discussions on the advantages of the ternary system over the binary system, and great interest was present on the ternary and more generally on the multi-valued logic systems in the academy.<ref>{{Cite conference |last1=Dubrova |first1=Elena |title=Multiple-Valued Logic in VLSI: Challenges and Opportunities |url=https://www.semanticscholar.org/paper/Multiple-Valued-Logic-in-VLSI:-Challenges-and-Dubrova/66d9ec85f74a953b3aa0b17758a306ce5035d29a |access-date=2025-05-27 |s2cid=17070721 }}</ref>

=== Advantages ===
Brusentsov found the ternary number system superior over the binary number system: it allowed him to create very simple and reliable elements, plus he needed seven times fewer elements than the Gutenmakher's computers. The power source requirements were also signficantly reduced because a smaller amount of magnetic rods and diodes was used. He also found the natural number-coding system used in the ternary system superior over the direct, reciprocal and supplementary number coding used in the binary system. He maintains that the ternary system is superior to binary in most aspects, published several papers advocating the ternary system during 1985-2014.

The symmetic nature of balanced ternary logic allows for natural representation of negative numbers.

The ternary system is also more efficient from an [[information theory]] persepctive. [[Donald Knuth]] wrote in his book ''The art of Computer Programming''  that "Perhaps the symmetric properties and simple arithmetic of this number system will prove to be quite important some day,"<ref name="Knuth">{{Cite book |last=Knuth |first=Donald |title=The art of Computer Programming |publisher=Addison-Wesley |year=1997 |isbn=0-201-89684-2 |volume=2 |pages=195–213 |authorlink=Donald Knuth}}</ref> noting that,{{blockquote|The complexity of arithmetic circuitry for balanced ternary arithmetic is not much greater than it is for the binary system, and a given number requires only <math>\log_3 2 \approx 63 \%</math> as many digit positions for its representation."<ref name="Knuth"/>}}In the paper ''The Prospects for Multivalued Logic: A Technology and Applications View'', [[Kenneth C. Smith]] argued that multi-valued logic is a solution to the interconnection problem in digital systems.<ref>{{Cite journal |last=Smith |date=September 1981 |title=The Prospects for Multivalued Logic: A Technology and Applications View |url=https://doi.org/10.1109/tc.1981.1675860 |journal=IEEE Transactions on Computers |volume=C-30 |issue=9 |pages=619–634 |doi=10.1109/tc.1981.1675860 |issn=0018-9340}}</ref> In particular, [[Douglas W. Jones|Douglas W.Jones]] suggests that the ternary system will reduce the number of interconnection wires by <math>36\%</math>.<ref name="Jones">{{Cite web |last=Jones |first=Douglas |date=April 1, 2012 |title=Douglas W. Jones on Ternary Computing |url=https://homepage.cs.uiowa.edu/~jones/ternary/ |access-date=2025-05-27 |website=homepage.cs.uiowa.edu}}</ref>

=== Disadvantages ===
Douglas W.Jones made a series of computations and designs algorithms of ternary system on his homepage under the name ''the Trenary Manifesto'', including fast ternary addition, multiplication, and division. It turns out that much of the improved efficiency in the interconnection and digit representation is balanced out by requiring more gates in the computations. For example, the ternary addition, while achieving the same computational speed as binary addition, requires <math>62\%</math> more logic.'''<ref name="Jones"/>'''

Meanwhile, many have suggested that ternary circuits are hard to develop, especially when most modern digital flows are binary.<ref name=":1">{{Cite journal |last1=Etiemble |first1=D. |last2=Israel |first2=M. |date=April 1988 |title=Comparison of binary and multivalued ICs according to VLSI criteria |url=https://doi.org/10.1109/2.49 |journal=Computer |volume=21 |issue=4 |pages=28–42 |doi=10.1109/2.49 |issn=0018-9162}}</ref><ref>{{Cite journal |last1=Nair |first1=Ravi |last2=Smith |first2=Scott |last3=Di |first3=Jia |date=2015-09-11 |title=Delay Insensitive Ternary CMOS Logic for Secure Hardware |journal=Journal of Low Power Electronics and Applications |language=en |volume=5 |issue=3 |pages=183–215 |doi=10.3390/jlpea5030183 |doi-access=free |issn=2079-9268}}</ref>

In the paper ''Comparison of Binary and Multivalued ICs According to VLSI Criteria'' written by Daniel Etiemble & Michel Israël, the authors compared binary and multivalued integrated circuits by examining their performance in detail, and discovered that while the design of multivalued circuits are valid and useful, they have not surpassed the binary circuits. They wrote in the conclusion that <ref name=":1" />{{blockquote|Multi-valued circuits and two-valued circuits must not
be seen as competitors. If they are seen as such, then two-valued circuits have already won.}}