Data Representation Part 3 HW3 1. Convert each decimal number to its 9's complement (use as many digits as shown): a) 73 b) 40512 c) 980034 d) Perform subtraction using 9's complement: 5042-671 2. Convert the following decimal numbers to the 10's complement: a) 128 b) 4097 c) 56020 d) Perform subtraction using 10's complement: 3205-4879 3. Perform the following multiplications. Assume that all values are unsigned numbers. (No problem with unsigned (always positive) numbers, just use the same standard techniques as in base 10.) a) 10112 × 01012 b) 011012 × 001112 c) 1100102 × 10112 d) 10110102 x 111012 4. Perform the following multiplications. Assume that all values are signed 2's complement numbers. a) 11002 01112 b) 00102 x 10102 - first multiply without sign-extending (show the wrong result), then redo with proper sign-extension. c) 111002 × 000112 5. Perform the following divisions. Assume that all values are unsigned numbers. a) 1011012 ÷ 1102 b) 1000112 ÷ 1012

From MATLAB Calculate the following scalars, matrices and vectors, using the matrices from problem 5. Outputs of the commands are required. (mean, sum, det, find, transpose (aka the apostrophe operator)

Modify the car purchase algorithm presented in class (on Chapter 1's slide set) so that the gasprice is no longer a constant, but instead it is subjected to an inflation of 5% yearly. Run thealgorithm and tabulate the costs year by year. (No need to program in C++ for this problemunless you really want to. You can use a spreadsheet or hand calculations.) Which car is abetter deal and by how much? Explain your algorithm welll.

Problem 12. Consider the following grammar: <S> → a <S> c <B> | <A> | b <A> → c <A> | c <B> → d | <A> Which of the following sentences are in the language generated by this grammar? a. abcd b. acccbd c. acccbcc d. acd e. accc

Problem 6. Using the grammar in Example 3.2, show a parse tree and a leftmost derivation for each of the following statements: a. A = A * (B + (C * A))

Problem 8. Prove that the following grammar is ambiguous: <S> → <A> <A> → <A> + <A> | <id> <id> → a | b | c

1 Mark for Review Consider the following class declaration. public class Sample { private int a; private double b; public Sample (int x, double y) { } a = x; b = yi } // No other constructors The following method appears in a class other than Sample. public static void test() { Sample object = new /* missing constructor call */ ; } APC Which of the following could be used to replace /* missing constructor call */ so that the method will compile without error? Highlights &

Consider the following class definition public class Bird private String species; private String color; private boolean canFly; public Bird(String str, String col, boolean ef) ' species str; color col; cantly cf; Autosaved at: 20:39:18 Mark for Review Which of the following constructors, if added to the Bird class, will cause a compilation error? public Bird() ' species "unknown"; color "unknown"; canFly false; public Bird(String col, String str). species str; color col; cantly false; public Bird (boolean ef, String str, String col) { species str color col; canFlyef; public Bird(String col, String str, boolean ef) > species str; color col; cantly ef; (0)

Problem A Add the 8-bit 2's-complement integer 01111111 to the 6-bit 2's-complement integer 011111. Sign-extend the 6-bit number to 8 bits. Add in binary and write the 8-bit result. State whether overflow occurred and how you know. Give the equivalent base-10 problem and result. Problem B Add the 7-bit 2's-complement integer 1010010 to the 5-bit 2's-complement integer 01110. Sign-extend the 5-bit number to 7 bits. Add in binary and write the 7-bit result. State whether overflow occurred and how you know. Give the equivalent base-10 problem and result. Problem C Add the 7-bit 2's-complement integer 1001110 to the 6-bit 2's-complement integer 100100. Sign-extend the 6-bit number to 7 bits. Add in binary and write the 7-bit result. State whether overflow occurred and how you know. Give the equivalent base-10 problem and result.