- Unary numeral system
The

**unary numeral system**is the bijective base-1numeral system . It is the simplestnumeral system to representnatural number s: in order to represent a number "N", an arbitrarily chosen symbol representing 1 is repeated "N" times. For example, using the symbol**|**(atally mark ), the number 6 is represented as**||||||**. The standard method of counting on one's fingers is effectively a unary system. Unary is most useful incounting or tallying ongoing results, such as the score in a game ofsport s, since no intermediate results need to be erased or discarded.Marks are typically clustered in groups of five for legibility. This is similar to the practice of using digit group separators such as spaces or commas in the

decimal system, to make large numbers such as 100,000,000 easier to read. The first or fifth mark in each group may be written at an angle to the others for easier distinction. Other example of a unary counting system clustered in counts of five is the Chinese,Japan ese andKorea nFact|date=June 2007 custom of writing theChinese character , Korean Hanja character, or Japanese kanji character which takes 5 strokes to write, one stroke each time something is added. In the fourth example depicted at left, the fifth stroke "closes out" a group of five, and is sometimes nicknamed the "herring bone" method of counting.In

Brazil ,France andGermany , a variation of this system is commonly used: Instead of arranging "sticks" in linear fashion, such as in the "herringbone" method, four marks are arranged to form a square, with the fifth mark crossing the square diagonally.Addition andsubtraction are particularly simple in the unary system, as they involve little more thanstring concatenation .Multiplication and division are more cumbersome, however.There is no explicit symbol representing zero in unary as there is in other traditional bases, so unary is a

bijective numeration system with a single digit. If there were a 'zero' symbol, unary would effectively be a binary system. In a true unary system there is no way to explicitly represent none of something, though simply making no marks represents it implicitly. Even in advanced tallying systems likeRoman numerals there is no zero character, instead the Latin word for 'nothing,' "nullae", is used.Compared to standard positional numeral systems, the unary system is inconvenient and is not used in practice for large calculations. It occurs in some

decision problem descriptions in theoretical computer science (e.g. someP-complete problems), where it is used to "artificially" decrease the run-time or space requirements of a problem. For instance, the problem ofinteger factorization is suspected to require more than a polynomial function of the length of the input as run-time if the input is given in binary, but it only needs linear runtime if the input is presented in unary. But this is potentially misleading: using a unary input is slower for any given number, not faster; the distinction is that a binary (or larger base) input is proportional to the base 2 (or larger base) logarithm of the number while unary input is proportional to the number itself; so while the run-time and space requirement in unary looks better as function of the input size, it is a worse function of the number that the input represents.For a real example of the unary system in ancient mathematics, see the

Moscow Mathematical Papyrus , dating from circa1800 BC .**ee also***

Church numeral **External links*** [

*http://www.research.att.com/~njas/sequences/A000042 Unary representation of natural numbers*] on the On-Line Encyclopedia of Integer Sequences.

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Numeral system**— This article is about different methods of expressing numbers with symbols. For classifying numbers in mathematics, see number system. For how numbers are expressed using words, see number names. Numeral systems by culture Hindu Arabic numerals… … Wikipedia**List of numeral system topics**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**Unary**— * Unary numeral system, the simplest numeral system to represent natural numbers * Unary operation, a kind of mathematical operator that has only one operand * Unary coding, an entropy encoding that represents a number n with n − 1 ones followed… … Wikipedia**Unary language**— In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1 k , where 1 can be any fixed symbol. For example, the language {1, 111, 1111} is unary, as is the… … Wikipedia**unary**— 1. adjective a) Consisting of or involving a single element or component. Negation is a unary operation. b) Of an operation, function, procedure or logic g … Wiktionary**Numeral (linguistics)**— This article is about the linguistic concept of words that represent numbers. For the mathematical notation for representing numbers of a given set, see Numeral system. In linguistics, number names (or numerals) are specific words in a natural… … Wikipedia**Non-standard positional numeral systems**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**Bijective numeration**— Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese … Wikipedia**List of mathematics articles (U)**— NOTOC U U duality U quadratic distribution U statistic UCT Mathematics Competition Ugly duckling theorem Ulam numbers Ulam spiral Ultraconnected space Ultrafilter Ultrafinitism Ultrahyperbolic wave equation Ultralimit Ultrametric space… … Wikipedia**Counting**— is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or… … Wikipedia