Introduction to Computer Science. Homework 1

Transcription

1 Introduction to Computer Science Homework. In each circuit below, the rectangles represent the same type of gate. Based on the input and output information given, identify whether the gate involved is an AND, OR, or XOR. (8 points) a. AND 0 0 b. OR 0 c. XOR 0 2. If the input and output bit patterns in the circuit below are interpreted as binary representations of numeric values, what operation does the circuit perform (8 points) (You would get only part of grade if your answer is not complete.) ANS: The circuit subtracts one (except for the case of the input being 000).

2 3. Solve each of the following problems by translating the values into two s complement notationn (using patterns of five bits), converting any subtraction problem to an equivalent addition problem, and performing that addition. (8 points) Example: a. - b. c. d. e. 4. Which of the following values cannot be represented accurately in the floating-point format introduced in the bel2w figure. (8 points) (If your answer only contains b or d, you would get half of grade) a. 6 2 b. 9 c. 3 6 d. 7 32

3 ANS: b would require too large of an exponent. d would require too many significant digits. 5. If a term paper consisted 42 pages, each containing 40 lines of 00 symbols each (counting each space as a symbol), was to be encoded using Unicode, how many bytes of storage space would be required (5 points) ANS: 336,000 bytes (68,000 symbols times 2 bytes per symbol) 6. Explain why adding only a few characters to a text file may increase the file s size by several hundred bytes and at other times may not increase the file s size at all. (5 points) ANS: File space is allocated in terms of physical records, each of which is several hundred bytes in size. Thus, the size of a file grows by physical record units rather than by byte size units. 7. In which of the following situations does an overflow never occur Justify an answer. (2 points) (8 points from the answer B, D. 4 points from the explanation of your answer) (a) Adding two positive integers (b) Adding one positive integer to a negative integer (c) Subtracting one positive integer from a negative integer. (d) Subtracting two negative integers. ANS: (a) Overflow can occur because the magnitude of the result is greater than the magnitude of each number and could fall out of the presentable range. (b) Overflow does not occur because the magnitude of the result is smaller than one of the numbers; the result is in the presentable range. (c) When we subtract a positive integer from a negative integer, the magnitudes of the numbers are added. This is the negative version of case a. Overflow can occur. (d) When we subtract two negative numbers, the magnitudes are subtracted from each other. This is the negative version of case b. Overflow does not occur. overflow does not occur in (b) and (d). 8. Multiple Choice Questions ( 單選題 ) (0 points) i. Which of the following is not contained in a CPU ANS: D

4 A. Instruction register B. Program counter C. General-purpose register D. Memory cell ii. In which of the following locations is information most readily available for manipulation by the CPU ANS: A A. General-purpose registers B. Main memory C. Mass storage iii. The bus in a computer is an example of which form of communication ANS: B A. Serial B. Parallel C. Neither A nor B iv. Which of the following instructions does not fall in the category of arithmetic/logic instructions ANS: D A. ROTATE B. ADD C. OR D. JUMP v. Which of the following is not an activity performed entirely within a CPU ANS: A A. Fetch instructions B. Perform Boolean operations C. Perform arithmetic operations D. Move data between registers 9. Describe the machine cycle. (9 points) ANS: Fetch an instruction and increment the program counter, decode the instruction, and execute the instruction. 0. Suppose three values x, y, and z are stored in a machine s memory. Describe the sequence of events (such as, loading registers from memory, saving values in memory, and so on) that leads to the computation (9 points) a. x + y + z b. (2x) + y ANS: To compute x + y - z, each of the values must be retrieved from memory and placed in a register, the sum of x and y must be computed and saved in another register, z must be subtracted from that sum, and the final answer must be stored in memory. A similar process is required to compute (2x) + y. The point of this example is that the multiplication by 2 is accomplished by adding x to x.. Suppose the memory cells at addressed 00 through 05 in the machine described in Appendix C of the textbook contain the following bit patterns:

5 (9 points) Address Content C Assuming the program counter initially contained 00, record (a) the contents of the program counter, (b) instruction register, and (c) memory cell at address 00 at the end of each fetch phase of the machine cycle until the machine halts. ANS: 2. Suppose the memory cells at addressed 00 through 0D in the machine described in Appendix C of the textbook contain the following bit patterns: (9 points) Address Contents B 09 0C 0A B0 0B 06 0C C0 0D 00 Assume that the machine starts with its program counter containing 00. (a) What bit pattern will be in register when the machine halts (b) What bit pattern will be in register 0 when the machine halts

6 (c) What bit pattern is in the program counter when the machine halts ANS: a. 03 b. 03 c. 0E