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TItest

Total questions: 77

Worksheet time: 39mins

Name
Class
Date
1.

... is a measure of uncertainty

a)

Encoding

b)

Entropy

c)

Information

d)

Redundancy

2.

{1,2,3,4,5,6} is the sample space of ...

a)

removing a card from the standard deck

b)

sum of two dice

c)

one dice roll

d)

one coin toss

3.

A card is drawn from a pack of 52 cards. The probability of getting a king of heart is

a)

1/26

b)

1/52

c)

1/13

d)

2/13

4.

A card is drawn from a pack of 52 cards. The probability of getting a queen or a king of heart is

a)

1/52

b)

1/26

c)

1/13

d)

2/13

5.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 001?

a)

101

b)

010

c)

001

d)

none

6.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 100?

a)

101

b)

010

c)

100

d)

none

7.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 000?

a)

010

b)

101

c)

000

d)

none

8.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 111?

a)

010

b)

101

c)

111

d)

none

9.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 011?

a)

010

b)

101

c)

011

d)

none

10.

A code has two allowable combinations 101 and 010. What is the allowable combination for the error combination 110?

a)

010

b)

101

c)

110

d)

none

11.

A fair coin is tossed four times, the probability of getting four heads is

a)

1/4

b)

1/16

c)

1

d)

1/2

12.

A Huffman code is a = 1, b = 000, c = 001, d = 01. Probabilities are p(a) = 0.4, p(b) = 0.1, p(c) = 0.2, p(d) = 0.3. The average length of codewords q is

a)

2.1 bit

b)

1.9 bit

c)

2.0 bit

d)

8.0 bit

13.

A redundancy of a code S = ...

a)

1 - Iavr/Imax

b)

Iavr/Imax

c)

1 + Iavr/Imax

d)

Imax/Iavr

14.

An alphabet consist of the letters a, b, c and d. The probability of occurrence is \n p(a) = 0.4, p(b) = 0.1, p(c) = 0.2 and p(d) = 0.3. The Huffman code is

a)

a=0,b=111,c=11,d=101

b)

a=0,b=110,c=111,d=10

c)

a=0,b=11,c=10,d=111

d)

a=01,b=111,c=110,d=10

15.

An average length of codewords qavr = ...

a)

∑ (pi * qi)

b)

∑ (pi / qi)

c)

∑ pi

d)

∑ qi

16.

An efficiency of a code E = ...

a)

Iavr/Imax

b)

Imax/Iavr

c)

Iavr/100

d)

Imax - Iavr

17.

ASCII code is a

a)

Variable length code

b)

Fixed length code

c)

Error-correction code

d)

None of the given

18.

Bag contain 10 black and 20 white balls, One ball is drawn at random. What is the probability that ball is white

a)

1

b)

2/3

c)

1/3

d)

4/3

19.

By the Bayes' rule for conditional entropy H(Y|X) \= ...

a)

[P(B|A)][P(A)] /P(B)

b)

H(X|Y) - H(X)

c)

H(X|Y)+ H(Y)

d)

H(X|Y) - H(X) + H(Y)

20.

By the Bayes' theorem ...

a)

P(B|A) = P(A and B)/P(A)

b)

P(B|A) = P(A and B)*P(A)

c)

P(A|B) = [P(B|A)][P(A)] /P(B)

d)

P(A|B) = [P(B|A)][P(A)] * P(B)

21.

By the Chain rule H(X,Y) \= H(Y|X) + ...

a)

H(Y)

b)

H(X)

c)

H(Y|X)

d)

H(X|Y)

22.

By the Hartley's formula the amount of information I = ...

a)

I = n*log m

b)

I = m*n

c)

I = log (m/n)

d)

I = log (m*n)

23.

By the Hartley's formula the entropy H = ...

a)

H \= - ∑(pi * log pi)

b)

H \= - ∑ (log pi)

c)

H \= log m

d)

H \= - ∑ (pi / log pi)

24.

By the property of joint entropy H(X,Y) <= ...

a)

H(X)

b)

H(Y)

c)

H(X) + H(Y)

d)

None of the given

25.

By the property of joint entropy H(X,Y) ...

a)

H(X,Y) >= H(X) and H(X,Y) <= H(Y)

b)

H(X,Y) <= H(X) and H(X,Y) >= H(Y)

c)

H(X,Y) >= H(X) and H(X,Y) >= H(Y)

d)

H(X,Y) >= H(X) + H(Y)

26.

By the Shannon's formula the amount of information I = ...

a)

H \= - n ∑( pi log pi)

b)

H \= - n * ∑ (log pi)

c)

H \= - n * ∑ pi

d)

H \= - n * ∑ (pi / log pi)

27.

By the Shannon's formula the entropy H = ...

a)

H \= - ∑( pi * log pi)

b)

H \= - ∑ (log pi)

c)

H \= - ∑ pi

d)

H \= - ∑ (pi / log pi)

28.

Calculate the code rate for Hamming (15,11) code

a)

1

b)

0,733

c)

0,571

d)

0,839

29.

Calculate the code rate for Hamming (31,26) code

a)

1

b)

0,733

c)

0,839

d)

0,571

30.

Calculate the code rate for Hamming (7,4) code

a)

1

b)

0,571

c)

0,733

d)

0,839

31.

Calculate the efficiency of the language if it has 32 letters and its I average is 1 bit.

a)

0,8

b)

0,2

c)

5

d)

1

32.

Calculate the redundancy of the language if it has 32 letters and its I average is 1 bit.

a)

0,8

b)

0,2

c)

5

d)

1

33.

Choose the formula to determine the number N of possible messages with length n if the message source alphabet consists of m characters, each of which can be an element of the message.

a)

N = mn

b)

N = nm

c)

N = m*n

d)

N = log m

34.

Code has dmin = 1. How many errors can be corrected by this code

a)

2

b)

3

c)

0

d)

1

35.

Code has dmin = 1. How many errors can be detected by this code?

a)

0

b)

2

c)

3

d)

1

36.

Code has dmin = 10. How many errors can be detected by this code?

a)

4

b)

8

c)

9

d)

10

37.

Code has dmin = 11. How many errors can be corrected by this code?

a)

11

b)

7

c)

5

d)

10

38.

Code has dmin = 11. How many errors can be detected by this code?

a)

5

b)

9

c)

10

d)

11

39.

Code has dmin = 12. How many errors can be detected by this code?

a)

5

b)

10

c)

11

d)

12

40.

Code has dmin = 2. How many errors can be corrected by this code?

a)

2

b)

3

c)

0

d)

1

41.

Code has dmin = 2. How many errors can be detected by this code?

a)

2

b)

3

c)

1

d)

0

42.

Code has dmin = 3. How many errors can be corrected by this code?

a)

2

b)

3

c)

1

d)

4

43.

Code has dmin = 3. How many errors can be detected by this code?

a)

1

b)

3

c)

2

d)

4

44.

Code has dmin = 4. How many errors can be detected by this code?

a)

5

b)

1

c)

3

d)

4

45.

Code has dmin = 5. How many errors can be corrected by this code?

a)

5

b)

3

c)

2

d)

4

46.

Code has dmin = 5. How many errors can be detected by this code?

a)

6

b)

2

c)

4

d)

5

47.

Code has dmin = 6. How many errors can be detected by this code?

a)

6

b)

2

c)

5

d)

4

48.

Code has dmin = 7. How many errors can be corrected by this code?

a)

5

b)

6

c)

3

d)

4

49.

Code has dmin = 7. How many errors can be detected by this code?

a)

7

b)

3

c)

6

d)

5

50.

Code has dmin = 8. How many errors can be detected by this code?

a)

8

b)

6

c)

7

d)

3

51.

Code has dmin = 9. How many errors can be corrected by this code?

a)

5

b)

7

c)

4

d)

8

52.

Code has dmin = 9. How many errors can be detected by this code?

a)

7

b)

9

c)

8

d)

4

53.

Code is optimal when ...

a)

qavr = H

b)

qavr ≠H

c)

qavr<H

d)

qavr >H

54.

Code rate R (k information bits and n total bits) is defined as

a)

k = n/R

b)

R = k * n

c)

R = k/n

d)

n = R * k

55.

Conditional entropy H(Y|X) lies between

a)

- H(Y) and 0

b)

0 and H(Y)

c)

- H(Y) and H(Y)

d)

0 and 1

56.

Conditional probability P(B|A) = ...

a)

P(A and B)/P(A)

b)

[P(B|A)][P(A)] /P(B)

c)

P(A and B)*P(A)

d)

[P(B|A)][P(A)] * P(B)

57.

Determine the Hamming distance for code that can detect 3 errors and correct 2 errors

a)

6

b)

5

c)

7

d)

9

58.

Determine the Hamming distance for code that can detect 3 errors and correct 1 errors.

a)

5

b)

4

c)

6

d)

8

59.

Determine the Hamming distance for code that can detect 5 errors and correct 3 errors.

a)

9

b)

8

c)

10

d)

14

60.

Encode a string "0000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0000001

b)

0000111

c)

0000000

d)

0000101

61.

Encode a string "0001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0001010

b)

0001001

c)

0001011

d)

0001111

62.

Encode a string "0010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0010010

b)

0010111

c)

0010110

d)

0010100

63.

Encode a string "0011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0011100

b)

0011001

c)

0011111

d)

0011101

64.

Encode a string "0100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0100011

b)

0100111

c)

0100110

d)

0100101

65.

Encode a string "0101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0101101

b)

0101000

c)

0101100

d)

0101110

66.

Encode a string "0110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0110101

b)

0110001

c)

0110000

d)

0110011

67.

Encode a string "0111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

0111110

b)

0111000

c)

0111010

d)

0111011

68.

Encode a string "1000" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1000111

b)

1000100

c)

1000101

d)

1000001

69.

Encode a string "1001" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1001111

b)

1001010

c)

1001110

d)

1001100

70.

Encode a string "1010" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1010010

b)

1010011

c)

1010001

d)

1010111

71.

Encode a string "1011" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3

a)

1011000

b)

1011100

c)

1011010

d)

1011001

72.

Encode a string "1100" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1100110

b)

1100000

c)

1100010

d)

1100011

73.

Encode a string "1101" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1101101

b)

1101011

c)

1101001

d)

1101000

74.

Encode a string "1110" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1110000

b)

1110101

c)

1110100

d)

1110110

75.

Encode a string "1111" with Hamming (7,4) code using the following structure (i1, i2, i3, i4, r1, r2, r3)

a)

1111110

b)

1111111

c)

1111101

d)

1111011

76.

Find the information amount of a symbol from the language with total number of symbols n = 18

a)

I = log218

b)

I = log182

c)

I = 18 * log218

d)

I = 18 * log182

77.

For a Hamming (15, 11) code, 15 is the total number of bits and 11 is the number of ...

a)

redundant bits

b)

data bits

c)

parity bits

d)

none of the given

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