9e. Convert your answer from (c) to its hexadecimal expansion.
1827 = 16 * 114 + 3
114 = 16 * 7 + 2
7 = 16 * 0 + 7
= (723) base 16
Check: 7 * 16^2 + 2 * 16^1 + 3 * 16^0 = (1827) base 10.
Page 2 of 9
9d. Convert the answer from (c) to its octal expansion.
1827 = 8 * 228 + 3
228 = 8 * 28 + 4
28 = 8 * 3 + 4
3 = 8 * 0 + 3
= (3443) base 8
Check: 3 * 8^3 + 4 * 8^2 + 4 * 8^1 + 3 * 8^0 = (1827) base 10
a. Determine the prime factorization of 1078 and 2541
1078= 1078/2= 539/7 = 77/11 = 7
= 1078 = 11*7^2*2
2541 = 2541/3= 847/7 = 121/11 = 11
= 2541= 11^2*7*3
b) determne the greatest common divisor
the common divisors are 3, 7, 11, also 77 because 7*11= 77
77= gcd(1078,2541)
c) determine the least common multiple
the common denominators 3 , 7, 11
3 = lcm(1078,2541)
9c. Convert the decimal expansion of (1827) base 10 to its binary expansion. Show your work.
1827 = 2 * 913 + 1
913 = 2 *456 + 1
456 = 2 * 228 + 0
228 = 2 *114 + 0
114 = 2 * 57 + 0
57 = 2 * 28 + 1
28 = 2 * 14 + 0
14 = 2 * 7 + 0
7 = 2 * 3 + 1
3 = 2 * 1 + 1
1 = 2 * 0 + 1
Check : (1 * 2^10 + 1 * 2^9 + 1 * 2^8 + 0 * 2^7 + 0 * 2^6 + 1 * 2^5 + 0 * 2^4 + 0 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1*2^0) = (1827) base 10.
(1827) base 10 = (11100100011) base 2.
6. Use the Euclidean algorithm to determine the greatest common divisor of 1078 and 2541. Show your work.
GCD (1078, 2541)
2541 = 2 * 1078 + 385
1078 = 2 * 385 +308
385 = 1 * 308 + 77
308 = 4 * 77 + 0
GCD (1078, 2541) = GCD (1078, 385) = GCD (385, 308) = GCD (308, 77) = GCD (77, 0) = 77
- Quiz #8 this Thursday will cover material/homework from sections 5.1 and 5.2.
- Test #3 will be given in class next Thursday, May 11. It will cover 4.5, 4.6, 10.1, 10.2, 10.4 , and 5.1-5.5.
- You are still welcome to add Test #2 Solutions posts to the OpenLab for participation credit; don’t forget to tag the “Test #2 Solutions” category.
- One of my homework problems from last Thursday’s class was to prove or disprove Kazi’s formula for 5.1 homework #10(a). I don’t have a record of my own boardwork from Thursday, so I can’t point out exactly where my mistake was. Kazi’s formula was correct. The proof is actually quite straightforward and I’ve attached a photo of my hand-written work to this post. Let me know if you have any questions.
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I hope everyone had a good break!
- Our regular office hours and class hours resume tomorrow (Tuesday).
- Bring the files for your MATLAB assignment with you to class tomorrow.
- Quiz #7 on Thursday will cover material/homework from 4.5, 4.6, 10.1, 10.2, and 10.4.
- There is a forum on campus at 12:45 tomorrow for students with questions/concerns about immigration rights. Information here. If this issue affects you or someone you know, I encourage you to attend the forum.
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ANSI NEOY SELE INSU LOBG CIKC ERHP
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