ME_2016_Spring_24_Homework_2
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Subject
Mechanical Engineering
Date
Feb 20, 2024
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ME 2016 - Computing Techniques (Spring 2024)
Homework 2 Due: January 31, 2024
Professionalism (4 pts) Points Report includes header/footer (name, date, course #, assignment #, page #) 2
Report is clearly legible 2
TOTAL
4
Problem 1 (20 pts) Points Part (a) correct work shown 5
Part (a) correct answer 5
Part (b) correct work shown 5
Part (b) correct answer 5
TOTAL
20 Problem 2 (30 pts) Points Part (a) correct work shown 5
Part (a) correct answer 5
Part (b) correct work shown 5
Part (b) correct answer 5
Part (c) correct work shown 5
Part (c) correct answer 5
TOTAL
30 Problem 3 (30 pts) Points Part (a) correct work shown 5
Part (a) correct answer 5
Part (b) correct work shown 5
Part (b) correct answer 5
Part (c) correct work shown 5
Part (c) correct answer 5
TOTAL
30
ME 2016 - Computing Techniques (Spring 2024)
Problem 4 (16 pts) Points List of practical guidelines 10 Definition
of
blunders
2
Definition
of
formulation
errors
2
Definition of data uncertainty 2
TOTAL
16 Total Points:
_______ /
100
2
ME 2016 - Computing Techniques (Spring 2024)
Homework 2 Due: January 31, 2024
Learning Objectives
•
To exercise your understanding of the base-10 and base-2 number systems.
•
To summarize strategies for mitigating roundoff and truncation error in numerical computations.
•
To summarize non-numerical sources of error that can arise in numerical computations.
Problem 1
Convert the following base-2 numbers to base-10 (show all work to receive full credit):
(a)
101011 (b)
110
.
01 Problem 2
Convert the following base-10 numbers to base-2 (show all work to receive full credit):
(a)
179 (b)
25 (c)
3.25 Problem 3
Consider a hypothetical floating point system in base-2 that uses 11-bit words. The system stores 1 digit for the sign, k = 5 digits for the exponent, and t = 5 digits for the fraction portion of the mantissa. Aside from the number of digits (bits), this floating point system follows all rules of the IEEE 754 standard. Answer the following questions about the hypothetical floating point system:
(a)
What are the lower and upper bounds, L and U , on the exponent for normalized numbers?
(b)
What is the approximate value of the largest positive normalized number that can be represented by this floating point system? (report your answer in base-10 with three significant digits)
(c)
What is the machine precision? (report your answer in base-10 with three significant digits)
Problem 4
(a)
Read section 4.3.2 of Chapra and Canale’s book (excerpt posted on Canvas) and summarize the practical guidelines to avoid numerical errors in computing.
(a)
Read section 4.4 (including 4.4.1-4.4.3) of Chapra and Canale’s book (excerpt posted on Canvas) and define blunders, formulation errors, and data uncertainty in the context of numerical methods.
1
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