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hw3 - n you obtain above satisfies t n ≥(7 2 n for all n...

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ECE 103 Discrete Math for Engineers University of Waterloo Spring 2010 Instructors: Koray Karabina, Ashwin Nayak Homework 3, due May 31, 2010 Note: The first three questions carry five marks, the last carries 10 marks. Question 1. Let t n denote the number of words of length n using the letters { A, B, C, D } such that no A is immediately followed by a B . Compute t 1 , t 2 . Find a recurrence relation for t n . Question 2. Prove by induction that the sequence
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Unformatted text preview: n you obtain above satisfies t n ≥ (7 / 2) n for all n ≥ 1. Question 3. Calculate 3 21 using Power , the recursive algorithm for exponentiation we learnt in class. Show all the steps in a tabular form. How many multiplications did you need? Question 4. Calculate 1420351 × 2104632 using the Karatsuba multiplication algorithm. Show all the steps in a tabular form, as in the lecture notes. 1...
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