Information/Word with Parity Bit

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ERROR DETECTION AND
CORRECTION CODES
Error Detection Code (Parity bit)
Error Correction Code ( Hamming Code)
ERRORS
While transferring information from one storage
media to another, error may occur due to uneven
magnetic surface or due to noise or failure.
 For Example: if transmitter sends 8-bit data
11100101.
 But receiver receives 8-bit as 11000101 due to
some noise or some other failure.
Error

11100101
Transmitter
11000101
Receiver
HOW TO DETECT THIS TYPES OF ERRORS ?
For detecting such type of errors, we use the
method of Parity in which an extra bit known as
parity bit or parity check bit is added with the
information/word.
 Now, we can send information or word either
using ODD parity or EVEN parity.
 For ODD parity, the parity bit is so choosen that
the total number of 1’s in each information or
word is always odd, including the parity bit.
 And for EVEN parity, the parity bit is so choosen
that the total number of 1’s in each information
or word is always even, including the parity bit.

ODD/EVEN PARITY BITS
Information/Word
11100011
10011100
11110111
10101011
10011100
11111110
Odd Parity (OP)
0
1
0
0
1
0
11100011
10011100
11110111
10101011
10011100
11111110
Even Parity (EP)
1
0
1
1
0
1
11100011
10011100
11110111
10101011
10011100
11111110
USE OF PARITY BIT
In previous example receiver do not know about
the error.
 Because there is no mechanism by which the
receiver detect the error.
 So what is the solution?
 By using parity bit receiver can easily detect the
error (one bit error).

PREVIOUS EXAMPLE WITH PARITY BIT

Suppose we are using ODD Parity System.
Error
11100101
11000101
Transmitter

Receiver
In order to generate parity bit we have to count
the number of 1’s present in the information at
transmitting end.
11100101
No of 1’s
We have 5 Ones (1’s)
PREVIOUS EXAMPLE WITH PARITY BIT
As we are using ODD Parity Bit System, and we
have 5 ones (1’s) in the information so the Parity
bit is?
 Answer: 0
 The information word with Parity Bit.

0 +
Parity Bit
11100101
011100101
Information/word
Information/Word
with Parity Bit
SEND THIS WORD TO THE RECEIVER
Suppose at receiving end the word is received as
011000101.
 Now the complete situation is like.....

Error
011100101
Transmitter
011000101
Receiver
INFORMATION AT RECEIVING END
011000101
Information at Receiving End


How to detect the error at Receiving End?
Again count the number of ones (1’s) at Receiving
End.
No of 1’s
011000101
We Have 4 Ones (1’s)
Information at Receiving End


As we are using ODD Parity Bit system so according
to that we have odd number of 1’s.
That means the data at receiving end is not correct.
ERROR DETECTION
Now we know that there is some error in the
information/word at receiving end.
 But what is the error and on which bit?
 How we can detect?


By using Hamming
codes.
ERROR CORRECTION CODE
By the use of Parity Bit we can just detect that,
the information/word at receiving end is not
correct.
 Because it is Error Detection Code.
 So the error detection code simple detect either
the information/word at receiving end is correct
or not. But it can’t correct the information/word.
 For this we need Error Correction Code.
 Hamming Code is one of the wall-known error
correction Code.

HAMMING CODE

Three Steps Before Transmission.
1.
Determine the number of Parity Bits to be added to
the given message bits.
2.
Determine the position of parity bits.
3.
Determine the position checked by the Parity bits.

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