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Objectives:
The objective
of this assignment is to enhance the learning capabilities of the students
about:
§ Redundancy
§ Block Coding
§ Hamming Distance
Question No. 1
(10 marks)
Suppose in a
code-word, we add two redundant bits to each 8-bit data word. Find the number of
1. Valid code-words
2. Invalid code-words
Answer:
To find the number of valid code words, we need
to find the number of ways to arrange the 10 bits (8 data bits + 2 redundant
bits) such that the code-word is valid. A code-word is considered valid if it satisfies the
constraint of having an even number of 1s.
We know that K called data-word r called redundant n called
code-word. So, in the scenario given
that 8 data word(k=8) and redundant bit
2 (r=2)
We find the number of code word by using this formula
Code Word formula
N =k + r
N = 8+2
N =10 (code
word)
For finding total number of code word, we applying formula
The number of possible codewords with n bits should be 2n
2n
210
1024 total
number of code word.
For finding valid number of code word, we skip redundant bit
(2)
28
256 valid code
words
Invalid code words=Total numbers of code words – valid code
words
Invalid code
words = 1024-256
Invalid code
words = 768
Question No.
2 (5
marks)
Calculate the Hamming distance given in the
below table for each of the following code words?
|
Code Words |
Hamming Distance |
|
d (10000, 00000) |
1 |
|
d (10101, 10000) |
2 |
|
d (00000, 11111) |
5 |
|
d
(00000, 00000) |
0 |
|
d
(000, 011) |
2 |
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