Deck 1: Data Representation

Question 1

Which of the following is the binary representation of 6 5/8?

A) 110.11
B) 10.011
C) 110.101
D) 100.101

Answer 1

C

Question 2

What is the result of the following addition problem (using two's complement notation)? $\begin{array} { r } 00001111 \\+ 10101010 \\\hline\end{array}$

A) 011000101
B) 10111001
C) 01010101
D) 10110101

Answer 2

10111001

Question 3

In which of the following addition problems (using two's complement notation)does an overflow error occur?

A) $\begin{array} { r } 0011 \\+ 1010 \\\hline\end{array}$
B) $\begin{array} { r } 1100 \\+ \quad 0100 \\\hline\end{array}$
C) $\begin{array} { r } 1100 \\+ 1100 \\\hline\end{array}$
D) $\begin{array} { r } 0100 \\+ 0100 \\\hline\end{array}$

Answer 3

$\begin{array} { r } 0100 \\+ 0100 \\\hline\end{array}$

Question 4

Which of the following representations in two's complement notation represents the smallest value?

A) 00000010
B) 11110000
C) 00000001
D) 11111111

Question 5

Which of the following mass storage system does not require physical motion?

A) Magnetic tape
B) Magnetic disk
C) CDs/DVDs
D) Flash drives

Question 6

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

Question 7

What is the result of the following subtraction problem (using two's complement notation)? $\begin{array} { r } 00001111 \\- \quad 10101010 \\\hline\end{array}$

A) 011000101
B) 10111001
C) 01010101
D) 10110101

Question 8

Which of the following bit patterns cannot be expressed in hexadecimal notation?

A) 11111111
B) 1001
C) 110011
D) 100000000001

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

Which of the following representations in two's complement notation represents the largest value?

A) 00000010
B) 11110000
C) 00000001
D) 11111111

Question 14

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

Question 15

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

Question 16

Which of the following Boolean operations produces the output 1 for the fewest number of input patterns?

A) AND
B) OR
C) XOR

Question 17

Which of the following bit patterns represents the value -9 in two's complement notation?

A) 00011010
B) 111110111
C) 10001001
D) 11111011

Question 18

Which of the following bit patterns represents the value 9 in two's complement notation?

A) 00011010
B) 11111011
C) 00001001
D) 11111011

Question 19

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

Question 20

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

Question 21

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 _________.

Question 22

Which of the following is a means of encoding music?

A) ASCII
B) MIDI
C) JPEG
D) GIF

Question 23

A7DF is the hexadecimal representation for what bit pattern?
____________

Question 24

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?
____________

Question 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

Question 26

How many different bit patterns can be formed if each must consist of exactly 6 bits?
____________

Question 27

What value is represented by each of the following patterns in excess notation?
A. 10000 ____
B. 0110 ____
C. 1100 ____

Question 28

When using two's complement notation,what bit pattern represents the negation of 01001010?
____________

Question 29

If the patterns 101.11 and 1.011 represent values in binary notation,what is the binary representation of their sum?
____________

Question 30

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

Question 31

Translate each of the following binary representations into its equivalent base ten representation.
A. 1100 __________
B. 10.011 __________
C. 0.01 __________
D. 10001 __________

Question 32

Represent the bit pattern 1111010010011011 in hexadecimal notation.
_________

Question 33

Using a two's complement notation system in which each value is represented by a pattern of six bits,represent the value -5.
____________

Question 34

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 __________

Question 35

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?
____________

Question 36

Using a two's complement notation system in which each value is represented by a pattern of six bits,represent the value 5.
____________

Question 37

How many bits are needed to represent 1024 different bit patterns?
____________

Question 38

In a two's complement system,what value is represented by the pattern 11111111111111001?
____________

Question 39

Which of the following is a possible LZW compression of the message "xyz xyz xyz"?

A) 1234
B) 1234545
C) 232
D) 12

Question 40

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

Question 41

Explain why the final version of the dictionary need not be transmitted with a message encoded using LZW compression.

Question 42

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?
____________

Question 43

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?

Question 44

Describe how a computer can produce an incorrect answer when performing numerical computations even though it has not malfunctioned.

Question 45

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.

Question 46

Describe how the concept of Hamming distance is used to produce an error-correcting code.

Question 47

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?

Question 48

What is frequency-dependent encoding?

Question 49

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
____________

Question 50

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
______________________________________

Question 51

Under what condition is each of the following data compression techniques most effective?
a.Run-length encoding
b.Relative encoding

Question 52

Explain why such terms as kilo,mega,and giga have acquired double meanings.

Question 53

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.

Question 54

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?

Question 55

To what does the term "normalized form" refer in the context of floating-point notation?

Question 56

Among the Boolean operations AND,OR,EXCLUSIVE OR,and NOT,which is least like the others? Explain your answer.

Question 57

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.)
____________

Question 58

The following is an error-correcting code in which any two patterns differ by a Hamming distance of at least three.

Decode each of the following patterns
010011 ________ 101010 ________ 011000 ________ 101101 _______

Question 59

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?
____________

Question 60

Construct the entire two's complement scale in which each value is represented by three bits.

Question 61

Why is the rightmost bit in a string of bits considered to be the least significant bit?

Question 62

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.

Question 63

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.

Question 64

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.