Problem 28E

a) Show that if a and b are positive integers with a ≥ b, then gcd(a, b) = a if a = b, gcd(a,b) = 2 gcd(a/2, b/2) if a and b are even, gcd(a, b) = gcd(a/2, b) if a is even and b is odd. and gcd(a, b) = gcd(a – b, b) if both a and b are odd.

b) Explain how to use (a) to construct an algorithm for computing the greatest common divisor of two positive integers that uses only comparisons, subtractions, and shifts of binary expansions, without using any divisions.

c) Find gcd(1202. 4848) using this algorithm.

Leslie Ogu COMM 1041 11/03/2016 - Chapter 8: Conversational Messages Homework ➢ Post the page numbers and information for your terms by 6pm tomorrow (terms were sent last night) ➢ Study for Exam 2 (TUESDAY) ➢ Team Teaching starts 11/10 Conversation ➢ Principle of process ➢ Principle of cooperation ➢ Principle of politeness ➢ Principle of dialogue ➢ Principle of turn taking Principle of Process ➢ 5 stages ○ Opening ○ Feedforward ○ Business ○ Feedback ○ Closing References to Get the Conversation Going ➢ Self-reference ○ Introducing yourself ○ Something referencing yourself ➢ Reference the other person ○ Have