Trinary System

The trinary system or ternary is the Numbering system base 3. The ternary Chiffre S are known under the name trit ( tr inary dig' it' ), in a way similar to bit.

Although most of the time, that refers to a system in which the three figures, 0, 1 and 2, are all of the integers Positif S, the adjective qualifies also the trinary system balanced , used for the logical comparison.

Base 3

Compared with the analog

Compared with base 10 and 2

/* Comparé with the base E *

Base 9 and 27

to see System nonaire and System septemvigésimal

Trinary computers

  • Setun
See also: Logical trinary

Balanced trinary notation

A trinary numbering system called balanced uses figures with values -1,0, and 1. This combination is especially invaluable for the ordinal relations between two values, where the three possible relations are lower than, equal, and higher than. The trinary one balanced is counted as follows: (in this example, the symbol 1 indicates figure -1, but in an alternative way for an easier use - can be used to indicate -1 and + to indicate +1.)

The trinary one not-balanced can be converted into trinary notation balanced by adding 1111. with reserve, then by withdrawing 1111… without reserve. For example, 0213 + 1113 = 2023, 2023 - 1113 = 1113 (ball) = 710.

The trinary one balanced is easily represented by the electronic signals, as potential being able to be is negative, neutral or positive. To use a third state includes/understands more data by figure; linear approximation log (3) /log (2) =~1,589 bits by trit.

The trinary one balanced has other applications. For example, a balances traditional with two plates, with a weight for each power of 3, can weigh relatively heavy objects with precision with a small number of weight, by moving the weights between the two plates and the table. For example, with weights for each power of 3 up to 81, an object of 60 G will be weighed perfectly with a weight of 81 G on the other plate, the weight of 27 G in the first plate, the weight of 9 G in the other plate, the weight of 3 G in the first plate, and the weight of 1 G remaining on side. This is an optimal solution in terms of many weights necessary to weigh any object. 60 = 11110

In a similar way, a balanced monetary system using the trinary one would save visits at the bank - the customers would like to have an exact transaction, or to have a small number of parts for the transaction, and the salesmen would need occasionally to deposit a large part or two. The system goes while representing the positive values for the parts which the customer gives to the merchant, and negative values for the parts that the merchant gives to the customer. For example, if a merchant sells an article for 5 zorkmid, the customer would give to the merchant a part of 9 zorkmid, and the merchant would give to the customer a part of 3 zorkmid and a part of 1 zorkmid.

Compact trinary representation

The trinary system east inefficient for the human use, just like the binary one. Consequently, the System nonaire (bases 9, each figure represents two basic digits 3) or the Système septemvigésimal (Base 27) (each figure represents 3 basic digits 3) is often used, in a way similar to the use of the octal Système and the hexadecimal Système in the place of the Binary system. The trinary system has also the equivalent of a Byte, called a Tryte.

Other resources

See too

  • Base 2

External bonds

  • Development of the ternary computers at the University of Moscow (in English)
  • Base third (in English)
  • Nikolay Brusentsov
  • Web pages on trinary balanced (in English)
  • the Arithmetic trinary one (in English)

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