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, 021_{3} + 111_{3} = 202_{3}, 202_{3}  111_{3} = 111_{3(bal)} = 7_{10}.
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 base3 digits) or base 27[?] (each digit is 3 base3 digits) is often used.
External Links Development of ternary computers at Moscow State University (http://www.computermuseum.ru/english/setun.htm) Third Base (http://www.americanscientist.org/issues/comsci01/compsci200111) 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.computermuseum.ru/english/setun.htm)
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