Write about hamming technique of error detection and correction in the case of a 4-bit data.



Hamming Technique (7,4) : In this case, we will have 4 bits of data and we will add 3 bits of redundant with the data by calculating the 4-bit data. For example, taking a 4-bit data as,



The encoder will encode the data as follows
,


Thus the decoder will receive,
0
1
1
0
0
1
1
And the decoder will decode the data to retrieve the original data along with detecting and correcting errors,

As the values of C4, C2, C1 are 0 then the received data has no error. Now to check error detection and correction applying a error in the data which was received by the decoder by changing a value of any bit. Here changing the value of the h5 bit from 1 to 0. So the data which will receive by the decoder will be as follows,
0
1
0
0
0
1
1
Now the decoder will decode again,


As the values of C4, C2, C1 are not all 0 then it will arrange the data as C4 C2 C1 = 101 and we know 101 is equivalent to 5, thus the decoder will confirm that the h5 bit has the error and it will change the value of h5, Thus the error detection and correction will be done.




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