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Unary coding, [nb 1] or the unary numeral system and also sometimes called thermometer code, is an entropy encoding that represents a natural number, n, with a code of length n + 1 ( or n), usually n ones followed by a zero (if natural number is understood as non-negative integer) or with n − 1 ones followed by a zero (if natural number is understood as strictly positive integer).
The unary numeral system is the simplest numeral system to represent natural numbers: [1] to represent a number N, a symbol representing 1 is repeated N times. [ 2 ] In the unary system, the number 0 (zero) is represented by the empty string , that is, the absence of a symbol.
The name "unary" comes from the fact that a unary language is the encoding of a set of natural numbers in the unary numeral system. Since the universe of strings over any finite alphabet is a countable set, every language can be mapped to a unique set A of natural numbers; thus, every language has a unary version {1 k | k in A}.
In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., p(i) ≥ p(i + 1) for all positive i), the expected lengths of the codewords are ...
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, [1] making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.
Unary function, a function that takes one argument; in computer science, a unary operator is a subset of unary function; Unary operation, a kind of mathematical operator that has only one operand; Unary relation, a mathematical relation that has one argument; Unary coding, an entropy encoding that represents a number n with n − 1 ones ...
The modern binary number system, the basis for binary code, is an invention by Gottfried Leibniz in 1689 and appears in his article Explication de l'Arithmétique Binaire (English: Explanation of the Binary Arithmetic) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern ...
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. [1] This is in contrast to binary operations , which use two operands. [ 2 ] An example is any function f : A → A {\displaystyle f:A\rightarrow A} , where A is a set ; the function f {\displaystyle f} is a unary operation on A .