Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 30 Dec 2017 My Price 5.00

Binary gcd algorithm

Binary gcd algorithm

Most computers can perform the operations of subtraction, testing the parity (odd or even) of a binary integer, and halving more quickly than computing remainders. This problem investigates the binary gcd algorithm, which avoids the remainder computations used in Euclid’s algorithm.

a. Prove that if a and b are both even, then gcd(a, b) = 2 .gcd(a/2, b/2).

b. Prove that if a is odd and b is even, then gcd(a, b) = gcd(a, b/2).

c. Prove that if a and b are both odd, then gcd(a, b) = gcd((a – b)/2, b).

d. Design an efficient binary gcd algorithm for input integers a and b, where a ≥ b, that runs in O(lg a) time. Assume that each subtraction, parity test, and halving takes unit time.

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Maurice Tutor
(5)
Status NEW Posted 30 Dec 2017 08:12 PM My Price 5.00

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