ass1sol - Introduction to Computer Engineering 1 Assignment...

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Introduction to Computer Engineering 1 Assignment 1 Data Representation Due Date: 5:00 PM Monday 25 th January 2010 Please submit this assignment by 5:00 pm on the due date via WebCT. Your assignment must be packaged as follows: Answers to Q1-Q4 in a Microsoft Word (doc/docx) or portable document format (pdf) file. The source code for Q5-Q6 in a text document (i.e. “.c” file). The output of your “C” programs (obtained either through screen capture or output re-direct) in the Microsoft Word or PDF file. All explanation for Q5-Q6 must be in the Microsoft Word or PDF. What to Hand In: 1 Microsoft Word or PDF document 2 .C files This Assignment will be marked out of 100 points. Late Submission will be accepted subject to a 5% penalty per day. No Assignments will be accepted past the Wednesday 27 th January 2010 of the week of submission. Question 1 (8 points) Convert the following integers into their numerical equivalents in the indicated bases (X refers to your answer, the subscript indicates the base). Be sure to use the correct number of significant figures for each case and show how the number of significant figures was obtained. Show all your work. (10 points) a) 124.123 5 i. X 2 ii. X 7 iii. X 9 iv. X 16 b) 38.837 10 i. X 2 ii. X 3 iii. X 5 iv. X 16 a) 1 5 2 + 2 5 1 + 4 5 0 + 1 5 1 + 2 5 2 + 3 5 3 = 39.304 i. 39/16 2r7 2/16 0r2 Integer part = 100111 #sign fig = log 2 5 3 = 6.965 = 7 0.304*16 4.864 0.864*16 13.824 01001101 124.123 5 = 100111.0100110 2
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ii. 39/7 5r4 5/7 0r5 Integer part = 54 #sign fig = log 7 5 3 = 2.48 = 3 0.304*7 2.128 0.128*7 0.896 0.896*7 6.272 206 124.123 5 = 54.206 7 iii. 39/9 4r3 4/9 0r4 Integer part = 43 #sign fig = log 9 5 3 = 2.19 = 3 0.304*9 2.736 0.736*9 6.624 0.624*9 5.616 265 124.123 5 = 43.265 9 iv. See part i) 124.123 5 = 27.4D 16 b) D i. 38/16 2r6 2/16 0r2 Integer part = 100110 #sign fig = 3/log 10 2 = 9.96 = 10 0.837*16 13.392 0.392*16 6.272 0.272*16 4.352 110101100100 38.837 10 = 100110.1101011001 2 ii. 38/3 12r2 12/3 4r0 4/3 1r1 1/3 0r1 Integer part = 1102
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#sign fig = 3/log 10 3 = 6.28 = 7 0.837*3 2.511 0.511*3 1.533 0.533*3 1.599 0.599*3 1.797 0.797*3 2.391 0.391*3 1.173 0.173*3 0.519 2111210 38.837 10 = 1102.2111210 3 iii. 38/5 7r3 7/5 1r2 1/5 0r1 Integer part = 123 #sign fig = 3/log 10 5 = 4.29 = 5 0.837*5 4.185 0.185*5 0.925 0.925*5 4.625 0.625*5 3.125 0.125*5 0.625 40430 38.837 10 = 123.40430 5 iv. Sfds See part i) 38.837 10 = 26.D64 5 Question 2 (9 points) What is the maximum and minimum number in the range of a 5-digit number for each of the following cases? Express all numerical answers in both the original base and its decimal (base-10) equivalent. For each case, also express the total number (in base-10) of distinct numbers that can be represented by the number scheme. Show all your work.
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ass1sol - Introduction to Computer Engineering 1 Assignment...

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