Decode the message 111010 110110 : Hamming Distance: The hamming distance between two bit patterns is the number of bits in which the patterns differ. An error correcting code is, Symbol Value represented A 000000 B 001111 C 010011 D 011100 E 100110 F 101001 G

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Answer 1

Expert Solution & Answer

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

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Answer 2

Expert Solution & Answer

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

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Answer 3

Expert Solution & Answer

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

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Answer 4

Expert Solution & Answer

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

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Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

Answer 8

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

Answer 9

Chapter 1, Problem 54CRP

a.

Explanation of Solution

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

Answer 10

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

Answer 11

b.

Explanation of Solution

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

Answer 12

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

Answer 13

c.

Explanation of Solution

Decode the message 011101 000110 000000 010100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 011101 matches with D of table 1 because 011101 and 011100 differ by one hamming distance.

The pattern 000110 matches with E of table 1 because 000110 and 100110 differ only by one hamming distance

Answer 14

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

Answer 15

d.

Explanation of Solution

Decode the message 010010 001000 001110 101111 000000 110111 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010010 matches with C of table 1 because 010010 and 010011 differ by one hamming distance.

The pattern 001000 matches with A of table 1 because 001000 and 000000 differ only by one hamming distance.

The pattern 001110 matches with B of table 1 because 001110 and 001111 differ only by zero hamming distance.

The pattern 101111 matches with B of table 1 because 101111 and 001111 differ only by one hamming distance

Answer 16

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

Answer 17

e.

Explanation of Solution

Decode the message 010011 000000 101001 100110:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 010011 matches with C of table 1 because 010011 and 010011 differ by zero hamming distance.

The pattern 000000 matches with A of table 1 because 000000 and 000000 differ only by zero hamming distance

Answer 18

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Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 1.1 - What input bit patterns will cause the following...Ch. 1.1 - In the text, we claimed that placing a 1 on the...Ch. 1.1 - Assuming that both inputs to the flip-flop in...Ch. 1.1 - a. If the output of an AND gate is passed through...Ch. 1.1 - Prob. 5QE Ch. 1.1 - Prob. 6QE Ch. 1.2 - If the memory cell whose address is 5 contains the...Ch. 1.2 - Prob. 2QE Ch. 1.2 - How many bits would be in the memory of a computer...Ch. 1.3 - Prob. 1QE

Symbol	Value represented
A	000000
B	001111
C	010011
D	011100
E	100110
F	101001
G

Decode the message 111010 110110 : Hamming Distance: The hamming distance between two bit patterns is the number of bits in which the patterns differ. An error correcting code is, Symbol Value represented A 000000 B 001111 C 010011 D 011100 E 100110 F 101001 G

Explanation of Solution

Decode the message 111010 110110: Hamming Distance: The hamming distance between two bit patterns is the number of bits in which the patterns differ. An error correcting code is, SymbolValue representedA000000B001111C010011D011100E100110F101001G

Explanation of Solution

Decode the message 101000 100110 001100: Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern. The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance

Explanation of Solution

Explanation of Solution

Explanation of Solution

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Chapter 1 Solutions

Decode the message 111010 110110:

Hamming Distance:

The hamming distance between two bit patterns is the number of bits in which the patterns differ.

An error correcting code is,

Symbol Value represented
A 000000
B 001111
C 010011
D 011100
E 100110
F 101001
G

Decode the message 101000 100110 001100:

Compare each pattern with the patterns in the code of table 1 until that pattern is found which is within a distance of one from the received pattern.

The pattern 101000 matches with F of table 1 because 101000 and 101001 differ by one hamming distance