Chapter One DATA STORAGE Answers to Some Problems in the book 2. a. upper input = 1, lower input = 0 6. 256 using two hexadecimal digits (16 bits) , 65536 using four hexadecimal digits (32 bits). 7. a. 11001011 b. 01100111 12. Data retrieval from main memory is much faster than from disk storage. Also data in main memory can be referenced in byte-sized units rather than in large blocks. On the other hand, disk storage systems have a larger capacity than main memory and the data stored on disk is less volatile than that stored in main memory. 14. There would be about 5,000 characters on the page requiring two bytes each (Unicode). So the page would require about 10,000 bytes or 10 sectors of size 1024 bytes. 18. About 7 years! 19. What does it say? 20. hexadecimal 21. a. 1 0 0 / 5 00110001 00110000 00110000 00101111 00110101 = 2 0 00100000 00111101 00100000 00110010 00110000 22. a. 31 30 30 2F 3D 20 3D 20 32 30 28. a. 0 b. 3 c. -3 d. -1 e. 7 29. a. 100 b. 111 c. 001 d. 011 e. 101 30. a. 15 b. -13 c. 13 d. -16 e. -9 32. a. 01101 b. 00000 c. 10000 (incorrect) d. 10001 e. 01110 f. 10011 (incorrect) g. 11110 h. 01101 i. 10000 (incorrect) j. 11111 33. a. 7 +1 becomes e. 12 +4 becomes 00111 + 00001 01000 which represents 8 01100 + 00100 10000 which represents -16 (overflow) f. 5 - 11 becomes 00101 - 01011 which converts to 00101 + 10101 11010 which represents -6 34. a. 3 1/4 b. 4 5/16 c. 13/16 d. 1 e. 2 1/8 35. a. 101.01 b. .0001 c. 111.111 d. 1.11 e. 110.101 36. a. 1 1/4 b. -1/2 c. 3/16 d. -9/32 37. a. 01001000 b. 01111111 c. 11101111 d. 00101010 e. 00011111 (truncation) 38. 00111100, 01000110, and 01010011 39. The best approximation of the square root of 2 is 1 3/8 represented as 01011011. The square of this value when represented in floating-point format is 01011111, which is the representation of 1 7/8. 40. The value one-eighth, which would be represented as 00101000. 41. Since the value one-tenth cannot be represented accurately, such recordings would suffer from truncation errors. 42. From left to right the result would be 23/4. From right to left the result would be 21/2. 43. a. 1 5/8 b. 4 c. 3 1/4 44. a. 01101100 b. 01101000 c. 01111000 (truncation) d. 01101011 45. a. The value is either eleven or negative five. b. A value represented in two's complement notation can be changed to excess notation by changing the high-order bit, and vice versa. 46. The value is two; the patterns are floating-point, excess, and two's complement, respectively. 47. a. This is the value -5 coded in floating-point, excess 8, and two's complement notation, respectively. b. This is the value -3 coded in two's complement, excess 128, and floating-point notation, respectively. c. This is the value 2 coded in excess 8, two's complement (or binary), and floating-point notation, respectively. 48. Only bit patterns of length 5 are valid excess 16 representations. Thus, 101, 010101, 1000, 000000, and 1111 are not valid. 49. b would require too large of an exponent. c would require too many significant digits. d would require too many significant digits. 50. When using binary notation, the largest value that could be represented would change from 15 to 255. When using two's complement notation the largest value that could be represented would change from 7 to 127. 51. 4FFFFF Some Exam Questions Multiple Choice Questions 1. Which of the following is the binary representation of 4 5/8? A. 100.11 ANSWER: D B. 10.011 C. 110.101 D. 100.101 2. Which of the following bit patterns represents the value 5 in two?s complement notation? A. 00011010 B. 11111011 C. 00000101 D. 11111011 ANSWER: C 3. In which of the following addition problems (using two?s complement notation) does an overflow error occur? A. 0011 + 1010 B. 0100 + 0100 C. 1100 + 1100 ANSWER: B 4. What value is represented by the bit pattern 01011100 when interpreted using floatingpoint format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa? A. -1 1/2 B. 1 1/2 C. -3/8 D. 3/8 ANSWER: B 5. Which of the following storage systems is best suited for storing and retrieving long strings of data that are processed in their sequential order? A. Main memory B. Magnetic disk C. Optical CDs and DVDs ANSWER: C 6. Assuming that each of the following bit patterns originally had even parity, which one contains an error? A. 10110100 B. 11000011 C. 00011000 D. 10001001 ANSWER: D 7. How many different symbols can be encoded using Unicode? A. 256 ANSWER: C B. 4,096 C. 65,536 D. 1,046,476 Fill-in-the-blank/Short-answer Questions 1. A computer?s main memory consists of numerous memory cells, each of which contains ________ bits. Each memory cell is identified by a numeric value called the cell?s _________. ANSWER: eight, address 2. Represent the bit pattern 1011010010011111 in hexadecimal notation. _________ ANSWER: B49F 4. How many different bit patterns can be formed if each must consist of exactly 6 bits? ____________ ANSWER: 64 7. If the patterns 101.11 and 1.011 represent values in binary notation, what is the binary representation of their sum? ____________ ANSWER: 111.001 10. What is the largest positive integer that can be represented in a two?s complement system in which each value is represented by eight bits? ____________ ANSWER: 127 (represented by 01111111) 12. When using two?s complement notation, what bit pattern represents the negation of 01101010? ____________ ANSWER: 10010110 14. Using an 8-bit floating-point format in which the most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa, write the bit pattern that represents the value 1 3/4. (Use normalized form.) ____________ ANSWER: 01011110 16. Which of the following addition problems cannot be solved accurately when using a floating-point system in which each value is encoded by a byte whose most significant bit is the sign bit, the next three bits represent the exponent field in excess notation, and the last four bits represent the mantissa? A. 2 1/2 + 1 3/8 B. 3 1/2 + 4 1/2 C. 7 + 3/4 ____________ ANSWER: A, B, and C Vocabulary (Matching) Questions Term Descriptive Phrase hexadecimal notation sector zoned-bit recording disk system buffer as a step An efficient way of representing bit patterns A segment of a track in a mass storage system A means of increasing the storage capacity of a magnetic ISO ANSI States flip-flop two?s complement notation floating-point notation fractions truncation pixel Unicode represented by 16 A storage area used to hold data on a temporary basis, often in transferring the data from one device to another An international organization for establishing standards A major standardization organization within the United A digital circuit capable of holding a single digit A means of encoding whole numbers A means of encoding numeric values that may involve An error that may occur when using floating-point notation A small part of an image A means of encoding text in which each symbol is bits General Format Questions 3. a. What is the output of the circuit below? b. In general, how does the three-bit input pattern across the top of the diagram relate to the circuit?s output? ANSWER: a. 0 b. The output is 0 if the input parity is odd; the output is 1 if the input parity is even. 6. Convert the following addition problem into two?s complement notation (using four bits per value), perform the addition, convert the answer back into base ten notation, and explain the results. 6 +3 ANSWER: In two?s complement notation the problem is to add 0110 and 0011. The sum is 1001 which translates to -7. This answer is incorrect due to overflow. 9. Construct the entire two?s complement scale in which each value is represented by three bits. ANSWER: 3 2 1 0 -1 -2 -3 -4 011 010 001 000 111 110 101 100 10. To what does the term ?normalized form? refer in the context of floating-point notation? ANSWER: Normalized form refers to a standard for positioning the bit pattern within the mantissa field. Many values can be represented in floating-point notation by different bit patterns, only one of which is in normalized form. Hence, restricting representations to normalized form assures that each value is represented by a unique pattern. 13. If a term paper consisted 42 pages, each containing 40 lines of 100 symbols each (counting each space as a symbol), was to be encoded using Unicode, how many bytes of storage space would be required? ANSWER: 336,000 bytes (168,000 symbols times 2 bytes per symbol) 14. 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. ANSWER: 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.