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# Ternary

Ternary is the base 3 numeral system. Ternary digits are known as trits, analogous to bit.

 Decimal 0 1 2 3 4 5 6 7 8 9 10 Ternary 0 1 2 10 11 12 20 21 22 100 101

Balanced Ternary Notation There is also a number system called balanced ternary, which uses digits with the values -1, 0, and 1. It works as follows. (I am using the symbol 1 to denote the digit -1.)

 Decimal -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Balanced ternary 110 111 11 10 11 1 0 1 11 10 11 111 110

Unbalanced ternary can be converted to balanced ternary notation by adding 1111.. with carry, then subtracting 1111... without borrow. For example, 0213 + 1113 = 2023, 2023 - 1113 = 1113(bal) = 710.

Balanced ternary is easily represented as electronic signals, as potential can either be negative, neutral, or positive. Utilizing the third previously ignored state allows for much more data per digit; linearly approximately log(3)/log(2)=~1.589 bits per trit.

Compact Ternary Representation Ternary is inefficient for human usage, just as binary is. Therefore, nonary[?] (base 9, each digit is two base-3 digits) or base 27[?] (each digit is 3 base-3 digits) is often used.

External Links Development of ternary computers at Moscow State University (http://www.computer-museum.ru/english/setun.htm) Third Base (http://www.americanscientist.org/issues/comsci01/compsci2001-11) Nikolay Brusentsov (http://www.icfcst.kiev.ua/museum/Brusentsov) Balanced Ternary Web Pages (http://perun.hscs.wmin.ac.uk/~jra/ternary/) Ternary Arithmetic (http://www.washingtonart.net/whealton/ternary) Development of ternary computers at Moscow State University (http://www.computer-museum.ru/english/setun.htm)

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