modular arithmetic
modular arithmetic (residue arithmetic) Arithmetic based on the concept of the congruence relation defined on the integers and used in computing to circumvent the problem of performing arithmetic on very large numbers.
Let m_{1}, m_{2},…, m_{k} be integers, no two of which have a common factor greater than one. Given a large positive integer n it is possible to compute the remainders or residues r_{1}, r_{2},…, r_{k} such that n ≡ r_{1} (mod m_{1}) n ≡ r_{2} (mod m_{2}) … n ≡ r_{k} (mod m_{k})
Provided n is less than m_{1} × m_{2} × … × m_{k}
n can be represented by (r_{1},r_{2},…,r_{k})
This can be regarded as an internal representation of n. Addition, subtraction, and multiplication of two large numbers then involves the addition, subtraction, and multiplication of corresponding pairs, e.g. (r_{1},…,r_{k}) + (s_{1},…,s_{k}) = (r_{1} + s_{1}, …, r_{k} + s_{k})
Determining the sign of an integer or comparing relative magnitudes are less straightforward.
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"modular arithmetic." A Dictionary of Computing. . Encyclopedia.com. 16 Aug. 2017 <http://www.encyclopedia.com>.
"modular arithmetic." A Dictionary of Computing. . Encyclopedia.com. (August 16, 2017). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/modulararithmetic
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residue arithmetic
residue arithmetic Another name for modular arithmetic.
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"residue arithmetic." A Dictionary of Computing. . Encyclopedia.com. 16 Aug. 2017 <http://www.encyclopedia.com>.
"residue arithmetic." A Dictionary of Computing. . Encyclopedia.com. (August 16, 2017). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/residuearithmetic
"residue arithmetic." A Dictionary of Computing. . Retrieved August 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/residuearithmetic