Homework 5 Solutions - Solutions to Homework Five CS 191...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Solutions to Homework Five CS 191 : Discrete Structures I Apr. 3 , Winter 2007 Due Date: Apr. 17, 2007, Tuesday, before the class meeting. Section 5.2, p205 In Exercise 26-31, express each hexadecimal number in decimal. Exercise (30) 209D Answer : (209D) 16 = 2 × 16 3 + 9 × 16 + 13 = 8349 Exercise (32) for (10) Express each binary number in Exercises 8-13 in hexadecimal. 11011011 Answer : (11011011) 2 = DB 16 Exercise (33) for (17) Express each decimal number in Exercise 14-19 in hexadecimal. 400 Answer : 16) 4 0 0 ……….. 0 (remainder) 16 ) 2 5 ……….. 9 16 )1 ……….. 1 0 Therefore, 400 10 = 190 16 Exercise (34) for (27) Express each hexadecimal number in Exercise 26, 27, and 29 in binary. 1E9 16 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Answer : 1 1110 1001 2 In Exercises 42-47, express each octal number in decimal. Exercise (43) (7643) 8 Answer : (7643) 8 = 7 × 8 3 + 6 × 8 2 + 4 × 8 + 3 = 3584 + 384 + 32 + 3 = 4003 2
Image of page 2
Section 5.3, p213 Use the Euclidean algorithm to find the greatest common divisor of each pair of integers in Exercises 1-10. Exercise (3) 220, 1400 Answer : 1400 mod 220 = 80 220 mod 80 = 60 80 mod 60 = 20 60 mod 20 = 0 Therefore, gcd (220, 1400) = 20 Exercise (11) for (3) For each number pair a, b in Exercises 1-10, find integer s and t such that sa + tb = gcd ( a , b ). 220, 1400 Answer : 1400 = 6 × 220 + 80 220 = 2 × 80 + 60 80 = 1 × 60 + 20 60 = 3 × 20 + 0 So, 20 = 80 – 60 = 80 – (220 - 2 × 80) = - 220 + 3 × 80 = - 220 + 3(1400- 6 × 220) = (-19) × 220 + 3 × 1400 Therefore, s = -19, t = 3. Another method (use matrix multiplications) From 1400 = 6 × 220 + 80, we have 80 220 = - 6 1 1 0 220 1400 From 220 = 2 × 80 + 60, we have 3
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
60 80 = - 2 1 1 0 80 220 From 80 = 1 × 60 + 20, we have 20 60 = - 1 1 1 0 60 80 Therefore, 20 60 = - 1 1 1 0 - 2 1 1 0 - 6 1 1 0 220 1400 = - - 3 1 2 1 - 6 1 1 0 220 1400 = - - 19 3 10 2
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern