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Assuming is the th Gray-coded bit (being the most significant bit), and is the th binary-coded bit (being the most-significant bit), the reverse translation can be given recursively: =, and =. Alternatively, decoding a Gray code into a binary number can be described as a prefix sum of the bits in the Gray code, where each individual summation ...
This translator is known as the Alpha Environment Software Translator (AEST), and it also supported translating VAX executables which had already been translated with VEST. [73] Two pre-production releases, OpenVMS I64 V8.0 and V8.1, were available on June 30, 2003, and on December 18, 2003.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.
Google Translate is a web-based free-to-use translation service developed by Google in April 2006. [12] It translates multiple forms of texts and media such as words, phrases and webpages. Originally, Google Translate was released as a statistical machine translation (SMT) service. [12] The input text had to be translated into English first ...
List of ISO 639 language codes. ISO 639 is a standardized nomenclature used to classify languages. [1] Each language is assigned a two-letter (set 1) and three-letter lowercase abbreviation (sets 2–5). [2] Part 1 of the standard, ISO 639-1 defines the two-letter codes, and Part 3 (2007), ISO 639-3, defines the three-letter codes, aiming to ...
Gottfried Wilhelm Leibniz or Leibnitz [a] (1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is disputed with Sir Isaac Newton to have invented calculus in addition to many other branches of mathematics, such as binary arithmetic, and statistics.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of statements within those systems.It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations such as addition and multiplication.
The manipulations of the Rubik's Cube form the Rubik's Cube group.. In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.