Deck 17: Information Science

Question 1

Using modular arithmetic, determine (42·17) mod 23.

Answer 1

1

Question 2

Use the Caesar cipher to decrypt the message DOO LV ZHOO.

Answer 2

ALL IS WELL

Question 3

Suppose you create a binary code by appending to each message word a₁ a₂ a₃ two parity-check digits c₁ = a₁ + a₂ and c₂ = a₂ + a₃. Will the resulting code detect and correct all single-digit errors?

Answer 3

It detects all singles, but doesn't correct all.

Question 4

Using modular arithmetic, determine (16·31) mod 41.

Question 5

Determine the value of s so that 11s = 1 mod 13.

Question 6

Create a binary linear code with eight possible code words that can detect and correct any single-digit error.

Question 7

Append a fourth check digit to each seven-digit code created by the Venn diagram method c₄ = a₁ + a₂ + a₃ + a₄. With this additional check digit, can double errors be detected and corrected?

Question 8

How does the weight of a code compare with the number of errors that can be detected?

Question 9

Create a binary linear code with four possible code words that can detect and correct any single-digit or double-digit error.

Question 10

Construct a code for five-digit binary message words that has four parity-check digits. Can it detect and correct single-digit errors?

Question 11

Suppose you create a binary code by appending to each message word a₁ a₂ a₃ a₄ three parity-check digits c₁ = a₁ + a₂ + a₄, c₂ = a₂ + a₃ + a₄, and c₃ = a₂ + a₃ + a₄. Will the resulting code detect and correct all single-digit errors?

Question 12

Construct a code for five-digit binary message words that has three parity-check digits. Can it detect and correct single-digit errors?

Question 13

Use the Caesar cipher to encrypt the message ABANDON HOPE.

Question 14

Give an example of a circumstance where the code C = {00000, 11111} could be of use.

Question 15

Determine the value of s so that 9s = 1 mod 17.

Question 16

For the message word a₁ a₂ a₃ a₄, append four check digits c₁ = a₁, c_{2 =} a₂, c₃ = a₃ and c₄ = a₄. Will the resulting code detect and correct all single-digit errors? Can double errors be detected and corrected?

Question 17

Using modular arithmetic, determine 17⁷ mod 41.

Question 18

Using modular arithmetic, determine 12⁷ mod 53.

Question 19

How does the weight of a code compare with the number of errors that can be corrected?

Question 20

Suppose you create a binary code by appending to each message word a₁ a₂ a₃ three parity-check digits c₁ = a₁ + a_{2 ,} c₂ = a₂ + a₃, and c₃ = a₁ + a₃. Will the resulting code detect and correct all single-digit errors?

Question 21

If the weight of a code is 5, how many errors can be detected?

Question 22

Use the nearest-neighbor Venn diagram method to decode the received word 1101101.

A) 1001
B) 0100
C) 1101
D) 1011

Question 23

Suppose the Venn diagram message 1110 is received as 1110001. Will the original message be recovered?

A) Yes
B) No

Question 24

Add the pair of binary sequences 1001010 and 1010010.

Question 25

What is the name of a cryptosystem that uses multiplication by a fixed value to shift each letter?

Question 26

Use the Venn diagram method to determine the code word of the message 1010.

A) 1010110
B) 1010111
C) 1010001
D) 1010011

Question 27

Suppose the Venn diagram coded message 1110 is received as 1110110. Will the original message be recovered?

A) Yes
B) No

Question 28

What is the minimum number of 1s that occur among all nonzero code words of that code called?

Question 29

Use the nearest-neighbor Venn diagram method to decode the received word 1011001.

A) 1011
B) 1010
C) 1001
D) 0010

Question 30

What is the name of the method that decodes a received message as the code word that agrees with the message in the most positions?

Question 31

Add the pair of binary sequences 1101001 and 1010011.

Question 32

Given that TROUT was used as the key word to encrypt ZFBY YBJVCGZ with the Vigenère cipher, decrypt the message.

Question 33

If the weight of a code is 8, how many errors can be corrected?

Question 34

If the weight of a code is 5, how many errors can be corrected?

Question 35

Use the Venn diagram method to determine the code word of the message 1001.

A) 1001111
B) 1001101
C) 1001001
D) 1001010

Question 36

Suppose mod 7 is equal to 0. Find mod 7.

Question 37

Use the nearest-neighbor Venn diagram method to decode the received word 1011000.

Question 38

Use the Vigenère cipher with the key word SPRING to encrypt the message APRIL SHOWERS.

Question 39

What is the distance between two strings of equal length?

Question 40

Suppose mod 7 is equal to 2. Find mod 7.

Question 41

You propose a code in which each two-digit binary message word a₁ a₂ has appended a parity-check digit c₁ = a₁ + a₂. Which of the following is a true statement?

A) The code can detect and correct any single-digit error.
B) The code can detect any single-digit error and correct some but not all single-digit errors.
C) The code can detect any single-digit error, but it cannot correct any single-digit error.
D) The code can detect some but not all single-digit errors.

Question 42

Use the Caesar cipher to decrypt the message ZHVW.

A) WEST
B) EAST
C) REST
D) another message

Question 43

You propose a code in which each three-digit binary message word a₁ a₂ a₃ has appended two parity-check digits c₁ = a₁ + a₂ and c₂ = a₂ + a₃. Which of the following is a true statement?

A) The code can detect and correct any single-digit error.
B) The code can detect any single-digit error and correct some but not all single-digit errors.
C) The code can detect any single-digit error, but it cannot correct any single-digit error.
D) The code can detect some but not all single-digit errors.

Question 44

Use the Caesar cipher to encrypt the message ROME BURNS.

A) URPH EXUQV
B) OLJB YROKP
C) HORU VQUXE
D) another sequence

Question 45

Add the binary sequences 0100110 and 1101010. How many 1s digits are in the sum?

A) 1
B) 3
C) 5
D) another answer

Question 46

Let C be the code {101010, 010101, 111111, 000000}. What is the weight of this code?

A) 0
B) 1
C) 3
D) 6

Question 47

Let C be the code {1100, 1010, 1001, 0110, 0101, 0011}. Which of the following is a true statement?

A) The code can detect and correct any single-digit error.
B) The code can detect any single-digit error and correct some but not all single-digit errors.
C) The code can detect any single-digit error, but cannot correct any single-digit error.
D) The code can detect some but not all single-digit errors.

Question 48

If two binary sequences that each have an even number of 1s are added, the sum:

A) will always have an even number of 1s.
B) will sometimes have an even number of 1s.
C) will always have an odd number of 1s.

Question 49

For the code C = {00000,11111}, how many errors would have to occur during transmission for a received word to be encoded incorrectly?

A) 2
B) 3
C) 4
D) 5

Question 50

Let C be the code {1010, 0101, 1111, 0000}. What is the weight of this code?

A) 0
B) 1
C) 2
D) 4

Question 51

Add the binary sequences 1001010 and 1010010. How many 1s digits are in the sum?

A) 2
B) 3
C) 4
D) another answer

Question 52

You propose a code in which each three-digit binary message word a₁ a₂ a₃ has appended a parity-check digit c₁ = a₁ + a₂ + a_3. Which of the following is a true statement?

A) The code can detect and correct any single-digit error.
B) The code can detect any single-digit error and correct some but not all single-digit errors.
C) The code can detect any single-digit error, but it cannot correct any single-digit error.
D) The code can detect some but not all single-digit errors.

Question 53

What is the distance between received words 1100101 and 1101010?

A) 1
B) 2
C) 3
D) 4

Question 54

Let C be the code {110, 101, 011, 000}. Which of the following is a true statement?

A) The code can detect and correct any single-digit error.
B) The code can detect any single-digit error and can correct some but not all single-digit errors.
C) The code can detect any single-digit error, but cannot correct any single-digit error.
D) The code can detect some but not all single-digit errors.

Question 55

You propose a code in which each digit of the message word is repeated to form the code word. For example, 101 is coded as 110011. Which of the following is a true statement?

A) The code can detect and correct any single-digit error and any double error.
B) The code can detect and correct any single-digit error and detect any double error, but cannot correct every double error.
C) The code can detect and correct any single-digit error, but it cannot detect every double error.
D) The code can detect any single-digit error, but it cannot correct every single-digit error.

Question 56

Use the encoding scheme A $\rightarrow$ 0, B $\rightarrow$ 10, C $\rightarrow$ 11 to encode the sequence ABACAB.

A) 010011010
B) 01011010
C) 01001101
D) another sequence

Question 57

What is the distance between received words 1001010 and 1010010?

A) 1
B) 2
C) 3
D) 4

Question 58

Use the encoding scheme A $\rightarrow$ 0, B $\rightarrow$ 10, C $\rightarrow$ 11 to decode the sequence 0101101011.

A) ABCABC
B) ABACABAC
C) ABCBCB
D) another sequence

Question 59

For the code C = {000000,111111}, how many errors would have to occur during transmission for a received word to be encoded incorrectly?

A) 2
B) 3
C) 4
D) 5

Question 60

For the code C = {000000, 000111, 111000, 111111}, how many errors would have to occur during transmission for a received word to be encoded incorrectly?

A) 1
B) 2
C) 3
D) 6

Question 61

Given that the following numbers were encoded using the delta function, which of the following is not an original number? 1130 QUOTE 6 QUOTE 12 QUOTE QUOTE

A) 1106
B) 1116
C) 1124
D) 1128

Question 62

Using modular arithmetic, 15³ mod 41 is equal to:

A) 0.
B) 13.
C) 31.
D) another number.

Question 63

Using modular arithmetic, 4³ mod 10 is equal to:

A) 2.
B) 4.
C) 6.
D) another number.

Question 64

Using modular arithmetic, (13·21) mod 12 is equal to:

A) 3.
B) 9.
C) 10.
D) another number.

Question 65

When using the Venn diagram for determining length seven binary code words for length four messages, which of the following are true statements? I: Every code word has an even number of 1s. II: Every possible string of seven binary digits is a code word.
III: Every possible string of seven binary digits can be read as a code word or a code
Word with a single-digit error.

A) I only
B) I and III only
C) II only
D) III only

Question 66

When using the Venn diagram for determining length seven binary code words for length four messages, what is the weight of the code?

A) 7
B) 3
C) 2
D) 1

Question 67

In Questions
What is the Huffman code for the symbol B?

A) 010
B) 011
C) 10
D) 11

Question 68

Using modular arithmetic, 13³ mod 34 is equal to:

A) 13.
B) 21.
C) 30.
D) another number.

Question 69

In Questions
What is the Huffman code for the symbol A?

A) 010
B) 011
C) 10
D) 11

Question 70

In Questions
What is the Huffman code for the symbol E?

A) 010
B) 011
C) 10
D) 11

Question 71

In Questions
What is the Huffman code for the message CAD?

A) 0001111
B) 1101100
C) 01001110
D) 1110011

Question 72

When using the Venn diagram for determining length seven binary code words for length four messages, what is the minimum distance between two code words?

A) 7
B) 3
C) 2
D) 1

Question 73

In Questions
What is the Huffman code for the symbol C?

A) 010
B) 011
C) 10
D) 11

Question 74

Using modular arithmetic, mod 17 is equal to:

A) 0.
B) 1.
C) 2.
D) another number.

Question 75

Given that the following numbers were encoded using the delta function, which of the following is not an original number? 89 0 9 QUOTE 6 QUOTE 10

A) 82
B) 88
C) 92
D) 98

Question 76

Given that the following numbers were encoded using the delta function, which of the following is not an original number? 95 QUOTE 8 QUOTE QUOTE 9 2

A) 81
B) 84
C) 90
D) 93

Question 77

Using modular arithmetic, 5³ mod 11 is equal to:

A) 0.
B) 4.
C) 7.
D) another number.

Question 78

C) 2.
D) another number.

Question 79

Using modular arithmetic, (13·21) mod 10 is equal to:

A) 2.
B) 3.
C) 7.
D) another number.

Question 80

Given that the following numbers were encoded using the delta function, which of the following is not an original number? 20437 547 QUOTE 211 62 503 QUOTE

A) 20007
B) 20267
C) 20330
D) 20984