 balanced ternary is a non-standard positional numeral system (a balanced form), useful for comparison logic. while it is a ternary (base&nbsp;3) number system, in the standard (unbalanced) ternary system, digits have values 0, 1 and 2. the digits in the balanced ternary system have values â1, 0, and 1. different sources use different glyphs used to represent the three digits in balanced ternary. in this article, t (which resembles a ligature of the minus sign and 1) represents â1, while 0 and 1 represent themselves. other conventions include using 'â' and '+' to represent â1 and 1 respectively, or using greek letter theta (Î), which resembles a minus sign in a circle, to represent â1. in setun printings, â1 is represented as overturned 1: "". ==computational properties== in the early days of computing, a few experimental soviet computers were built with balanced ternary instead of binary, the most famous being the setun, built by nikolay brusentsov and sergei sobolev. the notation has a number of computational advantages over regular binary. particularly, the plus-minus consistency cuts down the carry rate in multi-digit multiplication, and the rounding-truncation equivalence cuts down the carry rate in rounding on fractions. balanced ternary also has a number of computational advantages over traditional ternary. particularly, the one-digit multiplication table has no carries in balanced ternary, and the addition table has only two symmetric carries instead of three. a possible use of balanced ternary is to represent if a list of values in a list is less than, equal to or greater than the corresponding value in a second list. balanced ternary can also represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. ==conversion to decimal== in the balanced ternary system, the value of a digit n places left of the radix point is the product of the digit and 3n. this is useful when converting between decimal and balanced ternary. for instance, : 10bal. 3 = 1Ã31 + 0Ã30 = 310 : 10tbal. 3 = 1Ã32 + 0Ã31 + â1Ã30 = 810 : â910 = â1Ã32 + 0Ã31 + 0Ã30 = t00bal. 3 : 810 = 1Ã32 + 0Ã31 + â1Ã30 = 10tbal. 3 similarly, the first place to the right of the radix point holds 3â1 = 1/3, the second place to the right of the decimal place holds 3â2 = 1/9, and so on. for instance, : â2/310 = â1 + 1/3 = â1Ã30 + 1Ã3â1 = t.1bal. 3. {| border="1" cellpadding="4" align="center" cellspacing=
Computer_arithmetic Non-standard_positional_numeral_systems Ternary_computers