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Encyclopedia > Ternary numeral system
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## Contents

### Compared to decimal and binary

Representations of integer numbers in ternary do not get uncomfortably lengthy as quickly as in binary. For example, decimal 365 corresponds to binary 101101101 (9 digits) and to ternary 111112 (6 digits). However, they are still far less compact than the corresponding representations in bases such as decimal — see below for a compact way to codify ternary using nonary and septemvigesimal. The integers consist of the positive natural numbers (1, 2, 3, &#8230;) the negative natural numbers (&#8722;1, &#8722;2, &#8722;3, ...) and the number zero. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... Previous number: 364 Next number: 366 365 is a semiprime centered square number. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ...

Ternary Binary Decimal Ternary Binary Decimal Ternary 1 2 10 11 12 20 21 22 100 1 10 11 100 101 110 111 1000 1001 1 2 3 4 5 6 7 8 9 101 102 110 111 112 120 121 122 200 1010 1011 1100 1101 1110 1111 10000 10001 10010 10 11 12 13 14 15 16 17 18 201 202 210 211 212 220 221 222 1000 10011 10100 10101 10110 10111 11000 11001 11010 11011 19 20 21 22 23 24 25 26 27
Ternary Binary Decimal Power 1 10 100 1 000 10 000 1 11 1001 1 1011 101 0001 1 3 9 27 81 30 31 32 33 34 100 000 1 000 000 10 000 000 100 000 000 1 000 000 000 1111 0011 10 1101 1001 1000 1000 1011 1 1001 1010 0001 100 1100 1110 0011 243 729 2 187 6 561 19 683 35 36 37 38 39

As for rational numbers, ternary offers a convenient way to represent one third (as opposed to its cumbersome representation as an infinite string of recurring digits in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for the most basic fraction: one half (and thus, neither for one quarter, one sixth, one eighth, one tenth, etc.), because 2 is not a prime factor of the base. In mathematics, a rational number is a number which can be expressed as a ratio of two integers. ... A recurring or repeating decimal is a number which when expressed as a decimal has a set of final digits which repeat an infinite number of times. ... â€œIIâ€ redirects here. ... In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ... ...

Ternary Binary Decimal Fraction Ternary 0.111111111111... 0.1 0.020202020202... 0.012101210121... 0.011111111111... 0.010212010212... 0.1 0.010101010101... 0.01 0.001100110011... 0.00101010101... 0.001001001001... 0.5 0.333333333333... 0.25 0.2 0.166666666666... 0.142857142857... 1/2 1/3 1/4 1/5 1/6 1/7 0.010101010101... 0.01 0.002200220022... 0.002110021100... 0.002020202020... 0.002002002002... 0.001 0.000111000111... 0.000110011001... 0.000101110100... 0.000101010101... 0.000100111011... 0.125 0.111111111111... 0.1 0.090909090909... 0.083333333333... 0.076923076923... 1/8 1/9 1/10 1/11 1/12 1/13

### Compact ternary representation: base 9 and 27

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. Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... A Septemvigesimal numeral system has a base of twenty-seven. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0â€“9 and Aâ€“F, or aâ€“f. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... In computer science a byte is a unit of measurement of information storage, most often consisting of eight bits. ...

### Practical usage

A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a single hand for counting prayers (as alternative for the Misbaha). The benefit —apart from allowing a single hand to count up to 99 or to 100— is that counting doesn't distract the mind too much since the counter needs only to divide Tasbihs into groups of three. For people named Islam, see Islam (name). ... Tasbih (ØªØ³Ø¨ÙŠØ­) is a form of dhikr that involves the repetitive utterances of short sentences glorifying god. ... The hands (med. ... A Misbaha A Misbaha (Arabic: Ù…Ø³Ø¨Ø­Ø©) or Subha (Arabic:Ø³Ø¨Ø­Ø©) is a string of prayer beads, probably of Persian origin, which is traditionally used by Muslims to keep track of counting in Tasbih. ... Tasbih (ØªØ³Ø¨ÙŠØ­) is a form of dhikr that involves the repetitive utterances of short sentences glorifying god. ...

A rare ternary point is used to denote fractional parts of an inning in baseball. Since each inning consists of 3 outs, each out is considered $begin{matrix} frac{1}{3} end{matrix}$ (one third) of an inning and is denoted as .1. For example, if a player pitched all of the 4th, 5th and 6th innings, plus 2 outs of the 7th inning, his Innings pitched column for that game would be listed as 3.2, meaning $3 begin{matrix} frac{2}{3} end{matrix}$. (In this usage, only the fractional part of the number is written in ternary form.) An innings, or inning, is a fixed-length segment of a game in any of a variety of sports â€“ most notably baseball and cricket â€“ during which one team attempts to score while the other team attempts to prevent the first from scoring. ... This article is about the sport. ... In baseball, an out occurs when the defensive team effects any of a number of different events, and the umpire rules a batter or baserunner out. ... In baseball, innings pitched (IP) are the number of innings a pitcher has completed, measured by the number of batters and baserunners that are put out while the pitcher is in the game. ...

Ternary numbers can be used to convey self-similar structures like a Sierpinski Triangle or a Cantor set conveniently. Sierpinski triangle The Sierpinski triangle, also called the Sierpinski gasket, is a fractal, named after WacÅ‚aw SierpiÅ„ski who described it in 1916. ... The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one. ...

Ternary encoding can also be applied in most Relational Databases, with NULL acting as the third trit. By manually encoding datatypes it is possible to effectively reduce the storage requirements by a third.

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