WorksheetsPart 2 (51-100)
Total questions: 50
Worksheet time: 25mins
51. Code has dmin = 9. How many errors can be detected by this code?
7
9
8
4
52. Code rate R (k information bits and n total bits) is defined as
k = n/R
R = k * n
R = k/n
n = R * k
53. Conditional entropy H(Y|X) lies between
- H(Y) and 0
0 and H(Y)
- H(Y) and H(Y)
0 and 1
54. Convert the message into a signal suitable for transmission over the channel of communication,
referred to as …
Encoding
Decoding
Entropy
Redundancy
55. Determine the Hamming distance for code that can detect 3 errors and correct 2 errors.
6
5
7
9
56. Determine the Hamming distance for code that can detect 3 errors and correct 1 errors.
5
4
6
8
57. Determine the Hamming distance for code that can detect 5 errors and correct 3 errors.
9
8
10
14
58. Encode a string "0000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0000001
0000111
0000000
0000101
59. Encode a string "0001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2,
r3)
0001010
0001001
0001011
0001111
60. Encode a string "0010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0010010
0010111
0010110
0010100
61. Encode a string "0011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0011100
0011001
0011101
0011111
62. Encode a string "0100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0100011
0100110
0100111
0100101
63. Encode a string "0101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0101101
0101000
0101100
0101110
64. Encode a string "0110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0110101
0110011
0110001
0110000
65. Encode a string "0111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
0111110
0111000
0111010
0111011
66. Encode a string "1000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1000111
1000100
1000101
1000001
67. Encode a string "1001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1001111
1001010
1001110
1001100
68. Encode a string "1010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1010111
1010001
1010011
1010010
69. Encode a string "1011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1011100
1011010
1011000
1011001
70. Encode a string "1100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1100110
1100000
1100010
1100011
71. Encode a string "1101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1101101
1101011
1101001
1101000
72. Encode a string "1110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1110000
1110101
1110100
1110110
73. Encode a string "1111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
1111110
1111011
1111111
1111101
74. The length of the message is 16 symbols and the message’s alphabet consists of 4 symbols. Find the
amount of information in this message.
16
80
64
32
75. The efficiency of the language is 0,5 and its I average is equal to 1 bit. Calculate the number of letters
in this language’s alphabet?
64
32
4
16
76. Elements of alphabets X and Y are statistically related. It is known that H(X)=4 bits and H(Y)=10 bits.
What are a range of variation for a conditional entropy H(Y|X) when H(X|Y) changes from its min to
max?
(from 7 to 11)
(from 4 to 12)
(from 6 to 10)
(from 6 to 11)
77. For Hamming distance dmin and r errors in the received word, the condition to be able to detect the
errors is
dmin>= r+1
dmin>= 2r+1
dmin>= 2r+2
dmin>= r+2
78. For Hamming distance dmin and s errors in the received word, the condition to be able to correct
the errors is
dmin>= s+1
dmin>= 2s+1
dmin>= 2s+2
dmin>= s+2
79. Hamming (7,4) code can correct ___ error(s)
2
3
1
0
80. Hamming distance can easily be found with ...
XNOR operation
XOR operation
OR operation
AND operation
81. How does a noise affect the data?
change only the 0 to 1
change only the 1 to 0
change the 0 to 1 and the 1 to 0
None of the above
82.How many data bits are in the (15, 11) Hamming code?
A) 11
B) 4
C) 15
D) 5
11
4
15
5
83. How many data bits are in the (31, 26) Hamming code?
26
31
5
4
84. How many data bits are in the (7, 4) Hamming code?
4
3
7
10
85. How many parity bits are in the (15, 11) Hamming code?
4
15
11
5
86. How many parity bits are in the (31, 26) Hamming code?
26
31
5
4
87. How many parity bits are in the (7, 4) Hamming code?
3
4
7
11
88. A Huffman code is a = 0, b = 10, c = 110, d = 1110, e = 1111. Probabilities are p(a) = 0.50, p(b) = 0.30,
p(c) = 0.15, p(d) = 0.03, p(e) = 0.02. The average length of a code words is
1.75 bit
2.0 bit
1.3 bit
1.7 bit
89. Which letter will get the shortest codeword after Huffman coding of the word «bbaacccabaac»?
a
b
c
none
90. An alphabet consist of the letters a, b, c, d, e and f. The probability of occurrence is p(a) = 0.06, p(b)
= 0.15, p(c) = 0.4 and p(d) = 0.18, p(e)=0.17, p(f)=0.04. The Huffman code is
c=1,d=000,e=001,b=010,a=0110,f=0111
c=0,d=111,e=110,b=101,a=1001,f=1000
c=1,d=01,e=001,b=0000,a=00010,f=00011
c=1,d=01,e=001,b=000,a=0010,f=00011
c=0,d=101,e=110,b=101,a=1000,f=1001
91. If k - number of bits before Hamming encoding and n - number of bits after Hamming encoding then
k > n
k < n
k = n
k = 1/2 n
In digital communication system, smaller the code rate, ... are the redundant bits.
less
equal
more
unpredictable
93. Main idea of error control codes is
To add some redundancy
To delete some redundancy
To double all bits
None of the given
94. Noise affects ...
information source
receiver
channel
transmitter
95. Shannon-Fano and Huffman codes are an encoding algorithms used for
lossy data compression
lossless data compression
error correction
error detection
96. Specify the case when entropy is maximum
p1=0,5 and p2=0,5
p1=1 and p2=0
p1=0 and p2=1
p1=0,9 and p2=0,1
97. Specify the error position in the string "0001110", if the initial string was encoded with Hamming
(7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
i4
i1
i2
r2
98. Specify the error position in the string "1000110", if the initial string was encoded with Hamming
(7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
i1
i4
i2
i3
99. Specify the error position in the string "1001010", if the initial string was encoded with Hamming
(7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
r2
r1
r3
i3
100. Specify the error position in the string "1001100", if the initial string was encoded with Hamming
(7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)
r3
r2
r1
no error
