balanced ternary

Balanced Ternary (aka "Signary") is a method of numeric representation which expands on binary and is similar to trinary. It is based on the principle of trivalent logic and uses three distinct atomic values: +1 (logical true), 0 (logical unknown) and -1 (logical false). Note that false is represented here by -1, instead of 0 (zero) as with binary. Using signary as a means of data representation offers a number of advantages over other methods. For example, integer negation becomes a simpler process, merely requiring a logical inversion instead of the twos-compliment routine required by binary. Additionally, the concept of an unknown logic value provides a new dimension to logic operations.

Notation

There are several different methods of notation:

Logic Value	Numeric Value	Method 1	Method 2
true	+1	`+`	`1`
unknown	0	`0`	`0`
false	-1	`-`	`1`

For the purposes of this article, method 1 will be used.

Integer Representation

Integers can be represented using a similar method to binary. Unlike binary, however, negative numbers can use the same method and do not vary depending on the length of the data storage unit. The following table shows representations of all values from decimal -13 to decimal +13:

Decimal	Signary	Decimal	Signary	Decimal	Signary
-13	`---`	-4	`--`	5	`+--`
-12	`--0`	-3	`-0`	6	`+-0`
-11	`--+`	-2	`-+`	7	`+-+`
-10	`-0-`	-1	`-`	8	`+0-`
-9	`-00`	0	`0`	9	`+00`
-8	`-0+`	1	`+`	10	`+0+`
-7	`-+-`	2	`+-`	11	`++-`
-6	`-+0`	3	`+0`	12	`++0`
-5	`-++`	4	`++`	13	`+++`

Similarly to binary, the numeric value of each signary sequence can be determined from the sum of n x 3^p for each digit, where n is the numeric value of the digit and p is the position of the digit (p = 0 for the least significant digit, p = 1 for the next least significant digit, etc). For example:

Multiplier	3⁴	3³	3²	3¹	3⁰
Digit	`+`	`-`	`+`	`-`	`0`
Value	+81	-27	+9	-3	0	= 60

Also, it can be seen that negation requires a simple logical inversion, e.g. -11 = --+, +11 = ++-.

<< Previous

Word Browser

Next >>

altshausen
air niagara
free minded democratic league
drzymala car
liberal union (netherlands)
radical league
heads of government of krajina
ravensburg
thomas dowse
edge of darkness
zlatograd

freedom party (netherlands)
kami's lookout
cliffe at hoo
fusion saga
kay cottee
widecombe in the moor
burned in address
cradle board
spaceshipone flight 17p
botevgrad
michael wearing

kujukuri, chiba
naruto, chiba
sanbu, chiba
hasunuma, chiba
torrey canyon
matsuo, chiba
crumb (film)
yokoshiba, chiba
gabrovo
shibayama, chiba
sanbu district, chiba

internet security
in the mouth of the crocodile live in seattle
mutsuzawa, chiba
dravinja
chosei, chiba
shirako, chiba
nagara, chiba
mount seir
chonan, chiba
chosei district, chiba
cardiff blues