CDS Computing for Scientists. Final Exam Review. Final Exam on December 17, 2013

Transcription

1 CDS Computing for Scientists Final Exam Review Final Exam on December 17, Review Sheet 2. Sample Final Exam

2 CDS Computing for Scientists Final Exam - Review Sheet The following is a complete list of topics that will be covered in the Final exam. Tool: Introduction to MATLAB (MT) MT-CH1: Prologue MT-CH2: The MATLAB Environment MT-CH3: Assignments, Variables and Intrinsic Functions MT-CH4: Vectors and Vector Operations MT-CH5: Iteration I: FOR loops MT-CH6: Writing a Matlab Program MT-CH7: Basic Graphs and Plots MT-CH8: Matrices (Arrays) and Matrix Operations MT-CH9: Iteration II: Double Nested FOR Loops (DNFL) MT-CH10: Conditionals: IF Statements Section I: Computer Fundamentals (CF) CF-CH1: Binary Representation Positional Notation Binary to Decimal Conversion: Template Method Decimal to Binary Conversion: Template Method Decimal to Binary Conversion: Long Division Method Octal Numeral System; Hexadecimal Numeral System CF-CH2: Binary Operation Binary Addition Binary Subtraction CF-CH3: Binary Encoding/Decoding ASCII Code, ASCII Table Encoding ASCII Characters to Binary Sequences Decoding Binary Sequences to ASCII Characters CF-CH4: Logic Circuits and Logic Tables Logic Circuit Boolean Operation AND gate, AND table OR gate, OR table NOT gate, NOT table NAND gate, NAND table NOR gate, NOR table XOR gate, XOR table Logic Circuits with Three Inputs Binary Number Adding Machine CF-CH5: Data Storage Data density Bits, Bit Pattern, Bytes Transistors

3 Section II: Scientific Simulation (SS) SS-CH1: Introduction The Pipeline of Scientific Model, Mathematical Model and Computational Model SS-CH2: Computational Models Convert Scientific Model to Mathematical Model Convert Mathematic Model to Computational Model in MATLAB Predator-Prey Model: two unknowns SS-CH3: Simulation Basics Algorithm Iteration Initial Condition Interval SS-CH4: Integration Equation Integration to Summation: Sum of Areas of Rectangles Integration to Iteration: the Algorithm SS-CH4: Scientific Method Cycle of Measurement, Hypothesis, Prediction and Testing Section III: Visualization (VIS) VIS-CH1: Introduction VIS-CH2: Image As a 2-D Array Creating a Tumor Image Algorithms for Finding Two-in-Row, Two-in-Column, Left-B, and Right -B VIS-CH3: Color and Colormap Pseudo Color RGB Color System: Black, White, Gray; Red, Green, Blue; Yellow, Magenta, Cyan Colormap Method

4 CDS Computing for Scientists Final Exam - Sample Final Exam Final Exam on December 17, 2013 This is a closed-book closed-computer exam. Calculators are not allowed. Your answer should be on the space provided immediately following each question on the exam sheets. Feel free to use the backside if additional space is needed. Partial credit is given, if final answer is wrong but steps are shown. 1. Convert to its base ten equivalent using the template method 2. Convert to its binary equivalent using either the template method or long-division method. 3. Carry out the binary addition of ? Keep your answer in binary format 4. Carry out the binary subtraction of ? Keep your answer in binary format 5. What is the decimal value of 465 8? 6. What is the decimal value of character "B" in ASCII table? What is the binary number of character "B"? 7. Use ASCII code to encode the string "ASCII" into a binary sequence. Note that each character corresponds to 8 bits in binary number. 8. In the image below, four NANDS are connected and three of the inputs are set to 1. What are the values of Z and output if B = 1 and A = 0?

5 9. Fill out the logic table corresponding to the Logic Circuit shown below, which consists of a NAND gate and an OR gate. Show all input bit pattern combinations A, B and C in the table. For each input bit pattern combination, calculate the corresponding output. A B C output A B C Output 10. In a 7 bit analog to digital converter, how many different levels of data can be recorded? 11 For the matrix "A" shown below (1) How many rows and columns in this matrix? (2) What is value of A(2,1)? (3) What is value of A (1,3)? (4) What is value of A(2,2)+A(3,1)?

6 12. Considering the following iteration code, what is A(4)? A(1)=13; for i=[2:4] A(i)=A(i-1)+37; 13. Considering the following iteration code, what is A after the FOR loop? A(1)=0 for i=[1:5] A(i+1)=A(i)+i^2; The following statement is used for question 14, 15 My bank offers 5% interest on my account compounded yearly. Every year I deposit an additional $100. Assuming that on the first year your account had a balance of $ Translate the above statement into a mathematical model 15.Translate your mathematical model into MATLAB programming code. Your code should be able to calculate the balance in the next 10 years. There is no need of doing the calculation in the exam. Only MATLAB code is needed. 16. Briefly answer the following questions? (a) What is iteration? (b) what is algorithm? (c) What is initial condition? (d) What are the pros and cons if a smaller sub-interval is used in the iterative calculation?

7 17. f ( x) x F x dx Consider the integration of the function, f(x)=x 3, from the interval of x=0 to x=4. You are asked to make a numerical approximation of this integration using the rectangle method, that is to find the geometric area underneath the function with the sum of a series of rectangles. If you choose the sub-interval Δx=1, what is the approximated integration result? 18. One creates a 2-D array in Matlab using the following statement: >a=[3, 3, 3, 3; 1, 2, 3, 4; 4, 4, 4, 4; 5, 6,7, 8] How many rows in this 2-D array? What is value of a(3,2)? What is a(2,3)? 19. What is the array "a" after executing the following Double-nested For Loops? for i=[1:3] for j=[1:3] a(i,j)=i*j+2; 20. What is the array "A" after executing the following Double-nested For Loops? A = [1, 2, 3; 4, 5, 6; 7, 8, 9]; for m = [1:3] for n = [1:3] A(m,n) = m*n + 1;

8 21. What final value of c is printed out? c = 1; a = 1; b = 2; if(a + b < 3) c = c + 1; c 22. What final value of a, b, c is printed out? a = 4; b = 3; c = 10; if ( a < b && a < c) a = a + b + c; a if (a < b a < c) a = a + b + c; a b c 23. For the following 2-D images img = [ ]

9 (1) What is the pixel size of this image? (2) What is the value of pixel at img(2, 3)? (3) What is the value of pixel at img(4, 3)? (4) Write down the algorithm of finding two-in-rows? 24: Does a usual scientific data set have color or not, such as temperature data? Why is color used in visualization? 25. Describe the colors represented by the following [R, G, B] values (1) [0, 0, 0] (2) [1, 1, 1] (3) [0.3, 0.3, 0.3] (4) [1, 1, 0] (5) [0, 1, 1] 26. For the following colormap, MyColorMap=[ 1 1 1; ; 0 0 0] (1) How many colors in this colormap? (2) What are these colors?

10 1. ASCII Table Information Sheet 2. Logical Gates and Tables AND OR NOT NAND NOR XOR