Test Bank—Chapter One (Data Representation)
Multiple Choice Questions
1. Which of the following Boolean operations produces the output 1 for the fewest number of input
patterns?
A. AND B. OR C. XOR
2. Which of the following best describes the NOR operation?
A. An XOR followed by a NOT B. An OR followed by a NOT
C. A NOT followed by an OR C. An AND followed by a NOT
3. Which of the following bit patterns cannot be expressed in hexadecimal notation?
A. 11111111 B. 1001 C. 110011 D. 100000000001
4. Which of the following is the binary representation of 6 5/8?
A. 110.11 B. 10.011 C. 110.101 D. 100.101
5. Which of the following bit patterns represents the value 9 in two’s complement notation?
A. 00011010 B. 11111011 C. 00001001 D. 11111011
6. Which of the following bit patterns represents the value –9 in two’s complement notation?
A. 00011010 B. 111110111 C. 10001001 D. 11111011
7. What is the result of the following addition problem (using two’s complement notation)?
00001111
+ 10101010
A. 011000101 B. 10111001 C. 01010101 D. 10110101
8. What is the result of the following subtraction problem (using two’s complement notation)?
00001111
– 10101010
A. 011000101 B. 10111001 C. 01010101 D. 10110101
9. In which of the following addition problems (using two’s complement notation) does an overflow error
occur?
A. 0011 B. 1100 C. 1100 D. 0100
+ 1010 + 0100 + 1100 + 0100
10. Which of the following representations in two’s complement notation represents the largest value?
A. 00000010 B. 11110000 C. 00000001 D. 11111111
11. Which of the following representations in two’s complement notation represents the smallest value?
A. 00000010 B. 11110000 C. 00000001 D. 11111111
12. Which of the following bit patterns (represented in hexadecimal notation) represents a negative number
in two’s complement notation?
A. 3F B. 55 C. A6 D. 7E
13. Which of the following bit patterns (represented in hexadecimal notation) represents a positive number
in two’s complement notation?
A. 9F B. F7 C. A8 D. 7E
14. What value is represented by the bit pattern 01011100 when interpreted using 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?
A. -1 1/2 B. 1 1/2 C. –3/8 D. 3/8
15. Which of the following values cannot be stored accurately using a 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?
A. 2 1/2 B. 3/16 C. 7 D. 6 1/4
16. Which of the following bit-patterns represents the smallest value using the 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?
A. 01001000 B. 01011000 C. 00101000 D. 01111000
17. Which of the following data storage systems provides the most efficient random access to individual
data items?
A. Main memory B. Magnetic disk C. CDs/DVDs D. Flash drives
18. 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. CDs/DVDs
19. Which of the following mass storage system does not require physical motion?
A. Magnetic tape B. Magnetic disk C. CDs/DVDs D. Flash drives
20. Assuming that each of the following bit patterns originally had even parity, which one contains an
error?
A. 100110100 B. 110000011 C. 010011000 D. 100011001
21. How many errors per pattern could be corrected when using an error-correcting code in which any two
code patterns differ by a Hamming distance of 8?
A. 3 B. 4 C. 5 D. 6
22. Which of the following is a possible LZW compression of the message “xyz xyz xyz”?
A. 1234 B. 1234545 C. 232 D. 12
23. Which of the following systems is least efficient when encoding numeric values?
A. Two’s complement notation B. Excess notation
C. ASCII D. Floating-point notation
24. Which of the following is a means of encoding music?
A. ASCII B. MIDI C. JPEG D. GIF
25. Which of the following provides a compressed representation of an image by limiting the number of
different pixel colors to 256, thereby enabling each pixel in an image to be represented by a single byte
whose value indicates which of a palette of entries represents the pixel’s color?
A. ASCII B. MPEG C. JPEG D. GIF
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 _________.
2. Represent the bit pattern 1111010010011011 in hexadecimal notation.
_________
3. A7DF is the hexadecimal representation for what bit pattern?
____________
4. How many different bit patterns can be formed if each must consist of exactly 6 bits?
____________
5. How many bits are needed to represent 1024 different bit patterns?
____________
6. Translate each of the following binary representations into its equivalent base ten representation.
A. 1100 __________
B. 10.011 __________
C. 0.01 __________
D. 10001 __________
7. Rewrite each of the following values (represented in base ten notation) in binary notation.
A. 7 __________
B. 23 __________
C. 2 1/4 __________
D. 5/8 __________
8. If the patterns 101.11 and 1.011 represent values in binary notation, what is the binary representation of
their sum?
____________
9. Using a two’s complement notation system in which each value is represented by a pattern of six bits,
represent the value 5.
____________
10. Using a two’s complement notation system in which each value is represented by a pattern of six bits,
represent the value -5.
____________
11. 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?
____________
12. What is the smallest negative integer that can be represented in a two’s complement system in which
each value is represented by eight bits?
____________
13. In a two’s complement system, what value is represented by the pattern 11111111111111001?
____________
14. When using two’s complement notation, what bit pattern represents the negation of 01001010?
____________
15. What value is represented by each of the following patterns in excess notation?
A. 10000 ____ B. 0110 ____ C. 1100 ____
16. 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.)
____________
17. What is the largest value that can be represented in 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?
____________
18. 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
____________
19. The following is an error-correcting code in which any two patterns differ by a Hamming distance of at
least three.
Symbol Representation
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G 110101
H 111010
Decode each of the following patterns
010011 ________ 101010 ________ 011000 ________ 101101 _______
20. How many errors in a single code pattern could be corrected when using an error-correcting code in
which each code pattern is a Hamming distance of at least seven from any other code pattern?
____________
21. The following is a message that was originally encoded so that each pattern had odd parity. Circle the
patterns in which an error has definitely occurred.
101110101 111110000 100010010 000000000 111111111 010001000 100111101
______________________________________
22. Data compression techniques apply various principles to reduce the size of data. One, called
_______________________, avoids repeating long strings of the same data item. Another, called
_______________________, encodes the difference between consecutive blocks of data rather than
encoding each block in its entirety. Still another, called _________________________, uses short bit
patterns to encode frequently occurring items and longer patterns to encode less frequent items.
Vocabulary (Matching) Questions
The following is a list of terms from the chapter along with descriptive phrases that can be used to produce
questions (depending on the topics covered in your course) in which the students are ask to match phrases
and terms. An example would be a question of the form, “In the blank next to each phrase, write the term
from the following list that is best described by the phrase.”
Term Descriptive Phrase
bit Binary digit
Boolean operation AND, OR, XOR, NOT
address A numeric value used to identify a memory cell
hexadecimal notation An efficient way of representing bit patterns
track A circle on the surface of disk platter on which data is written/read
sector A segment of a track in a mass storage system
cylinder A set of tracks at a given position of the read/write heads
seek time The time required to move the read/write heads from one track to
another
latency time The average amount of time required for the desired data to rotate
around to the read/write head
transfer rate The rate at which data can be written to or read from a device
zoned-bit recording A means of increasing the storage capacity of a magnetic disk system
ISO An international organization for establishing standards
ANSI A major standardization organization within the United States
ASCII A system developed by the American Standards Institute for encoding
text.
flip-flop A digital circuit capable of holding a single digit
two’s complement notation A means of encoding whole numbers
floating-point notation A means of encoding numeric values that may involve fractions
truncation An error that may occur when using floating-point notation
pixel A small part of an image
GIF A means of compressing an image file by restricting the number of
colors available
JPEG A means of compressing images by blurring the boundaries between
different colors while maintaining all brightness information
Unicode A means of encoding text in which each symbol is represented by 21
bits which may be encoded in UTF-8, UTF-16, or UTF-32 formats.
SD card An application of flash technology
Flash memory A mass storage device that traps electrons in tiny chambers of silicon
dioxide
LZW An example of adaptive dictionary encoding
MIDI A means of encoding music in terms of notes and instruments rather
than actual audio
VLSI A means of constructing complex circuitry in a very small space.
General Format Questions
1. Describe how a computer can produce an incorrect answer when performing numerical computations
even though it has not malfunctioned.
2. Describe how the concept of Hamming distance is used to produce an error-correcting code.
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?
4. 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?
5. Explain why such terms as kilo, mega, and giga have acquired double meanings.
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
7. Under what condition is each of the following data compression techniques most effective?
a. Run-length encoding
b. Relative encoding
8. What is frequency-dependent encoding?
9. Construct the entire two’s complement scale in which each value is represented by three bits.
10. To what does the term “normalized form” refer in the context of floating-point notation?
11. Explain why the final version of the dictionary need not be transmitted with a message encoded using
LZW compression.
12. Among the Boolean operations AND, OR, EXCLUSIVE OR, and NOT, which is least like the others?
Explain your answer.
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?
14. In a two’s complement system, what value can be added to any other value without causing an
overflow? How many values in the system have this property? Explain your answer.
15. Why is the rightmost bit in a string of bits considered to be the least significant bit?
16. Given that 1 foot = .3048 meters, write a Python script that will convert a height given in feet and
inches to a height given in meters.
17. Given that 1 foot = .3048 meters, write a Python script that will convert a height given meters to a
height given in feet and inches.
