Computer Science 15-111 (Sections A & B), Spring 2007

Homework #2 (part 1)

Due: Mon 22-Jan-2007 as you enter class.

The following problems are to be solved without use of a calculator or a computer. Work them by hand. (This is what you will need to do on upcoming quizzes and tests!).

What to submit: A hardcopy of your answers, labeled “15-111 hw 2 part 1”, with your name, section, and CA’s name all clearly denoted at the top of the page.

1. Express -122 in 8-bit 2’s complement (that is, as a signed byte).

2. For what value of x does ((byte) 137) == x) evaluate to true?

3. Convert 0xE3 to binary, octal, and decimal.

4. Convert decimal 173 to binary, octal, and hexadecimal.

5. We know that (1 + 2 + 4 + 8 + ... + 2ⁿ) + 1 = 2⁽ⁿ⁺¹⁾. Rewrite this statement in binary (rather than decimal) and briefly explain why writing it this way makes it plainly true.

6. In just a few words of plain English, assuming n and m are positive int’s, describe under what conditions x will be set to true in this code:
boolean x = (n / m * m == n);

7. For what two values of byte b does (((byte)-b) == b)) evaluate to true?

8. In Two’s Complement, the number 111…1 always represents what decimal number?

9. The following code will not loop forever. Very briefly, why not?

int x = 1;
while (x > 0) x++;

10. What will the following code print out?
int a = 68, b = 3;
int x = a++ - --b;
System.out.printf("%c%c%3d",x,a,b);

11. What will the following code print out?
System.out.println(1 + '2' % 3 * 4);