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The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
The final digit of a Universal Product Code, International Article Number, Global Location Number or Global Trade Item Number is a check digit computed as follows: [3] [4]. Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.
These complications mean that there are three common ways to express a polynomial as an integer: the first two, which are mirror images in binary, are the constants found in code; the third is the number found in Koopman's papers. In each case, one term is omitted. So the polynomial + + may be transcribed as:
Data binning, also called data discrete binning or data bucketing, is a data pre-processing technique used to reduce the effects of minor observation errors.The original data values which fall into a given small interval, a bin, are replaced by a value representative of that interval, often a central value (mean or median).
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The term "binary file" is often used as a term meaning "non-text file". [2] Many binary file formats contain parts that can be interpreted as text; for example, some computer document files containing formatted text, such as older Microsoft Word document files, contain the text of the document but also contain formatting information in binary ...
.xlt – Legacy Excel templates; officially designated "Microsoft Excel 97–2003 Template".xlm – Legacy Excel macro; OOXML Office Open XML (OOXML) format was introduced with Microsoft Office 2007 and became the default format of Microsoft Excel ever since. Excel-related file extensions of this format include:.xlsx – Excel workbook