Ternary numeral system

A ternary /ˈtɜːrnəri/ numeral system (also called base 3) has three as its base. This means that you can only count with 0, 1, and 2. The first ten numbers (from 0 to 9) in ternary are 00, 01, 02, 10, 11, 12, 20, 21, 22, 100. When all the digits in the number reach 2, you add a 1 in front and change everything else to 0. There is another system with the same name more specifically called the balanced ternary system. This system is called that way because 0 is the middle digit, with the other two digits being -1 and 1. That system is used in comparison logic and ternary computers.

Numeral systems by culture
Hindu–Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou Counting rods	Japanese Korean
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Greek (Ionian) Āryabhaṭa
Other systems
Attic Babylonian Egyptian Etruscan	Mayan Roman Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…

A ternary multiplication table

×	1	2	10	11	12	20	21	22	100
1	1	2	10	11	12	20	21	22	100
2	2	11	20	22	101	110	112	121	200
10	10	20	100	110	120	200	210	220	1000
11	11	22	110	121	202	220	1001	1012	1100
12	12	101	120	202	221	1010	1022	1111	1200
20	20	110	200	220	1010	1100	1120	1210	2000
21	21	112	210	1001	1022	1120	1211	2002	2100
22	22	121	220	1012	1111	1210	2002	2101	2200
100	100	200	1000	1100	1200	2000	2100	2200	10000

Similar to a bit in binary, a ternary digit is called a trit.

Ternary Numeral System Media

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  Use of ternary numbers to balance an unknown integer weight from 1 to 40 kg with weights of 1, 3, 9 and 27 kg (4 ternary digits actually gives 34 = 81 possible combinations: −40 to +40, but only the positive values are useful)

Related pages

• Octal
• Duodecimal
• Hexadecimal