Although ternary most often refers to a system in which the three numerals, zero, one and two, are all positive integers, the adjective also leads its name to the balanced ternary system, in which case it is useful for those seeking the representation of both positive and negative numbers. It would also supposedly be of use to a race of creatures with three digits or three arms; Marc Okrand, in fact, has stated that the Klingon language runs on a ternary system.

Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Ternary | 0 | 1 | 2 | 10 | 11 | 12 | 20 | 21 | 22 | 100 | 101 |

Table of contents |

2 Balanced Ternary Notation 3 Compact Ternary Representation 4 External Links |

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} = 1__1__1_{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.