Homework 2: Data Storage AMS 103, Fall 2023 Due: Monday, October 2, 8:30 am EDT Objectives...

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Homework 2: Data Storage AMS 103, Fall 2023 Due: Monday, October 2, 8:30 am EDT Objectives Quiz: Wednesday, October 4, 9:30 am EDT To reinforce concepts relevant to digital devices, storing data on digital devices, and the underlying mathematical techniques. To practice quantitative skills related to base systems and logarithms. Instructions List, on the first page, any students with whom you worked and/or any outside resources you used in preparing your solutions. You may not use solutions to previous semesters' homework assignments. Generative AI (such as chatGPT) is not recommended. If used, make sure to cite and attribute it as you would any other source. You should not just copy and paste text from generative AI. Clearly identify which problem you are solving at the start of the solution. Solutions must be clearly and logically presented. When applicable, show your work! The solution to each problem must be continuous; that is, parts should not be crossed out and solutions to other problems should not be interspersed. Your solutions must be submitted through Brightspace as a single PDF file. Scans of legibly written pages are fine. Improperly submitted or late homework will not receive credit. Grading Policy This assignment will be graded for both completeness and accuracy. Completion of the assignment-did you attempt every problem?-will be worth 50% of the score. Select problems will also be graded for accuracy; that is, did you provide a correct answer and, when applicable, show your work? Accuracy will determine the remaining 50%. Remember, if you use Wolfram AlphaTM (or another software tool), include a screen shot with both input and pertinent output to show your work. Also, wikipedia is not a valid source (although it may be a great starting point to find more acceptable sources!). Problems 1. (*, 14 pts) What is a FLOP? What does a computer's FLOP rate (FLOP per unit time) measure? What computer had the highest FLOP rate in June 2023? What was its FLOP rate? (Hint: Use the "Rmax" information on the top 500 list). 2. (*, 14 pts) Quantum computing is a proposed technology that uses very small objects (atoms or molecules) instead of transistors to execute instructions. You can read more about it at https: //www.explainthatstuff.com/quantum-computing.html. What is one advantage of a quantum computer over a conventional computer? Are quantum computers generally regarded as superior to conventional computers? Explain. Homework 2: Data Storage Page 2/2 3. (, 22 pts) The concept of discretization helps convert an image to a sequence of Os and 1s. Give an example of a quantity that must be discretized when converting a music file to 0s and 1s. Explain your response. 4. (*, 14 pts) Consider the bits 101110. (a) Assume the bits encode a non-negative integer (using binary numbers). Convert this number to decimal. (b) Suppose instead that these bits encoded a number using 6-bit 2's complement. What would it be in decimal? 5. (*, 22 pts) We saw in lecture methods to store integers (both negative and non-negative) and real numbers as sequences of Os and 1s. Integers can be stored exactly (using binary numbers and/or 2's complement), but real numbers must be approximated by rational numbers. In decimal (base 10), a rational number can be expanded as, for example, That is, 11 = 1.375. 8 11 8 1 x 100+ 3 x 10-1 +7 x 10-2 +5 x 10-3. In a similar fashion, we can expand a rational number in binary, 11 =%23 20 + % 21+ #23 2 2 + #2 23 + ... 8 = 1 x 20+0x21+1 x 2-2 +1 x 2-3. Thus, we can write 11/8 as 1.011 in binary; thereby converting it to a sequence of Os and 1s (and a decimal binary?-point). (a) Is 0.01 the binary expansion of 1/2? Explain why or why not. (b) Determine the binary expansion of 27/4. Remember that a rational number is a number that can be written as a ratio of integers, such as 1/2, 3/4, and 5/1. 6. (*, 14 pts) What text is encoded by the following sequence of ASCII codes (given in base 10)? 87 111 119 46 32 84 104 105 115 32 105 115 32 42 65 110 78 111 121 105 110 103 33 42 Homework 2: Data Storage AMS 103, Fall 2023 Due: Monday, October 2, 8:30 am EDT Objectives Quiz: Wednesday, October 4, 9:30 am EDT To reinforce concepts relevant to digital devices, storing data on digital devices, and the underlying mathematical techniques. To practice quantitative skills related to base systems and logarithms. Instructions List, on the first page, any students with whom you worked and/or any outside resources you used in preparing your solutions. You may not use solutions to previous semesters' homework assignments. Generative AI (such as chatGPT) is not recommended. If used, make sure to cite and attribute it as you would any other source. You should not just copy and paste text from generative AI. Clearly identify which problem you are solving at the start of the solution. Solutions must be clearly and logically presented. When applicable, show your work! The solution to each problem must be continuous; that is, parts should not be crossed out and solutions to other problems should not be interspersed. Your solutions must be submitted through Brightspace as a single PDF file. Scans of legibly written pages are fine. Improperly submitted or late homework will not receive credit. Grading Policy This assignment will be graded for both completeness and accuracy. Completion of the assignment-did you attempt every problem?-will be worth 50% of the score. Select problems will also be graded for accuracy; that is, did you provide a correct answer and, when applicable, show your work? Accuracy will determine the remaining 50%. Remember, if you use Wolfram AlphaTM (or another software tool), include a screen shot with both input and pertinent output to show your work. Also, wikipedia is not a valid source (although it may be a great starting point to find more acceptable sources!). Problems 1. (*, 14 pts) What is a FLOP? What does a computer's FLOP rate (FLOP per unit time) measure? What computer had the highest FLOP rate in June 2023? What was its FLOP rate? (Hint: Use the "Rmax" information on the top 500 list). 2. (*, 14 pts) Quantum computing is a proposed technology that uses very small objects (atoms or molecules) instead of transistors to execute instructions. You can read more about it at https: //www.explainthatstuff.com/quantum-computing.html. What is one advantage of a quantum computer over a conventional computer? Are quantum computers generally regarded as superior to conventional computers? Explain. Homework 2: Data Storage Page 2/2 3. (, 22 pts) The concept of discretization helps convert an image to a sequence of Os and 1s. Give an example of a quantity that must be discretized when converting a music file to 0s and 1s. Explain your response. 4. (*, 14 pts) Consider the bits 101110. (a) Assume the bits encode a non-negative integer (using binary numbers). Convert this number to decimal. (b) Suppose instead that these bits encoded a number using 6-bit 2's complement. What would it be in decimal? 5. (*, 22 pts) We saw in lecture methods to store integers (both negative and non-negative) and real numbers as sequences of Os and 1s. Integers can be stored exactly (using binary numbers and/or 2's complement), but real numbers must be approximated by rational numbers. In decimal (base 10), a rational number can be expanded as, for example, That is, 11 = 1.375. 8 11 8 1 x 100+ 3 x 10-1 +7 x 10-2 +5 x 10-3. In a similar fashion, we can expand a rational number in binary, 11 =%23 20 + % 21+ #23 2 2 + #2 23 + ... 8 = 1 x 20+0x21+1 x 2-2 +1 x 2-3. Thus, we can write 11/8 as 1.011 in binary; thereby converting it to a sequence of Os and 1s (and a decimal binary?-point). (a) Is 0.01 the binary expansion of 1/2? Explain why or why not. (b) Determine the binary expansion of 27/4. Remember that a rational number is a number that can be written as a ratio of integers, such as 1/2, 3/4, and 5/1. 6. (*, 14 pts) What text is encoded by the following sequence of ASCII codes (given in base 10)? 87 111 119 46 32 84 104 105 115 32 105 115 32 42 65 110 78 111 121 105 110 103 33 42