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.