Ternary numeral system
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Ternary or trinary is the base-3 numeral system. Ternary digits are known as trits (trinary digit), with a name analogous to "bit". Although ternary most often refers to a system in which the three digits, 0, 1, and 2, are all nonnegative integers, the adjective also lends its name to the balanced ternary system, used in comparison logic and ternary computers.
Comparison to other radixes
Compared to base 10 and 2
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Binary | 0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 |
| Ternary | 0 | 1 | 2 | 10 | 11 | 12 | 20 | 21 | 22 | 100 | 101 |
Compact ternary representation: base 9 and 27
Ternary is inefficient for human usage, just as binary is. Therefore, nonary (base 9, each digit is two ternary digits) or septemvigesimal (base 27, each digit is three ternary digits) is often used, similar to how octal and hexadecimal systems are used in place of binary. Ternary also has a unit similar to a byte, the tryte, which is six ternary digits.
A base-three system isn't necessarily inefficient for human usage. It is used in Islam to count to 100 on a single hand for worship (as alternative for the rosary in Christianity). The benefit—apart from allowing a single hand to count up to 100—is that counting doesn't distract the mind too much since you only need to count to three. Once one has to count to four, counting would become exceedingly challenging.
External links
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