modular arithmetic

collocation in English

meaningsofmodularandarithmetic

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations witharithmetic.
modular
adjective
uk
/ˈmɒdʒ.ə.lər/us
/ˈmɑː.dʒə.lɚ/
consisting of separate parts that, when combined, form a ...
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arithmetic
noun[U]
uk
/əˈrɪθ.mə.tɪk/us
/əˈrɪθ.mə.tɪk/
the part of mathematics that involves the adding and multiplying, etc. ...
See more atarithmetic

(Definition ofmodularandarithmeticfrom theCambridge English Dictionary© Cambridge University Press)

Examplesofmodular arithmetic

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He further advancedmodulararithmetic, greatly simplifying manipulations in number theory.
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For example, inmodulararithmetic, consider the equivalence relation on the integers defined by if is a multiple of a given integer, called the "modulus".
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These can be of quite general use, for example inmodulararithmeticor powering of matrices.
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Considerations related tomodulararithmetichave led to the notion of valuation ring.
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A great convenience ofmodulararithmeticis that it is easy to multiply, though quite difficult to add.
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Another advantage of this convention is in the use ofmodulararithmeticas implemented in modern computers.
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Modulararithmeticis often used to calculate checksums that are used within identifiers.
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Note how the elements are non-negative because of themodulararithmetic.
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This is a simple consequence of the laws ofmodulararithmetic; we are simply saying that we may first reduce "a" modulo "p".
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It is used in polynomial factorization, a problem for which all known efficient algorithms usemodulararithmetic.
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It is even more efficient to usemodulararithmetic, which reduces the problem to a similar one over a finite field.
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The corresponding addition and multiplication of equivalence classes is known asmodulararithmetic.
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It then usesmodulararithmeticto transform the integer that each plaintext letter corresponds to into another integer that correspond to a ciphertext letter.
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When working withmodulararithmetic, each equivalence class is usually represented by its common residue, for example which can be found using long division.
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The product cipher combines a sequence of simple transformations such as substitution, permutation, andmodulararithmetic.
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These values may be modeled mathematically as the five numbers 0, 1, 2, 3, or 4 inmodulararithmeticmodulo 5.
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A familiar use ofmodulararithmeticis in the 12-hour clock, in which the day is divided into two 12-hour periods.
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Instead of rewriting the current symbol, it can perform amodulararithmeticincrementation on it.
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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Go to the definition ofmodular
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See other collocations witharithmetic