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 = 111_3(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.html) Nikolay Brusentsov (http://www.icfcst.kiev.ua/museum/Brusentsov.html) Balanced Ternary Web Pages (http://perun.hscs.wmin.ac.uk/~jra/ternary/) Ternary Arithmetic (http://www.washingtonart.net/whealton/ternary.html) Development of ternary computers at Moscow State University (http://www.computer-museum.ru/english/setun.htm)