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+8 votes

Following 7 bit single error correcting hamming coded message is received.

Determine if the message is correct (assuming that at most 1 bit could be corrupted). If the message contains an error find the bit which is erroneous and gives correct message.


asked in Computer Networks by Veteran (67.7k points) | 660 views

5 Answers

+7 votes
Best answer

Here Answer is yes. There is error in This message. Error is in bit 6.

How to calculate it ? First of all reverse given input to get it in correct position from 1 to 7.


Bit 1, Bit 2 & Bit 4 are partity bits.

Calculating position of error =>

c3 c2 c1

1   1   0

Here c1 = bit4⊕bit5⊕bit6⊕bit7=0⊕0⊕0⊕1=1 (Taking Even parity )

        c2  = bit2⊕bit3⊕bit6⊕bit7=1⊕1⊕0⊕1=1

        c3 = bit1⊕bit3⊕bit5⊕bit7=0⊕1⊕0⊕1=0

Ref ->,4%29

When you correct bit 6 .

You get message as 0110011.

IF you calculate C1,c2,c3 all will be 0 now !


answered by Veteran (46.8k points)
selected by

See example here..

good read if u want to grasp it completely.

@Rajesh This link is so "Big" to read :P
if assume odd parity then bit 1 has error ,it should be zero
by default which one to choose odd or given ?
+1 vote
6th bit is having error both parity bit 2 and 4 support this so 6 bit need to be 1 and data must be 1100110
answered by (45 points)
+1 vote

Error bit is 6 ... Msg is 1100110


answered by Loyal (4k points)
0 votes
Answer: Bit 5 has the error. It should be 1.

Here, parity bits are 1,2,4 (power of 2).

Hamming code based on data bits received = 110
Bit 1 = Bit 3 $\oplus$ Bit 5 = 1 $\oplus$ 0 = 1. (XOR of all bits having the least significant digit as 1)
Bit 2 = Bit 3 $\oplus$ Bit 6 = 1 $\oplus$ 0 = 1. (XOR of all bits having the second least significant digit as 1)
Bit 7 = Bit 4 $\oplus$ Bit 5 $\oplus$ Bit 6 = 0 $\oplus$ 0 $\oplus$ 0 = 0. (XOR of all bits having the third least significant digit as 1)

But the received message has Bit 1 = 0, Bit 2 = 1, Bit 7 = 1 (Actual hamming code)

Bit error = Hamming code based on data bits received $\oplus$ Actual hamming code = 110 $\oplus$ 011 = 101 (i.e. Bit 5 has the error)
answered by Veteran (35.5k points)

the answer is should be bit 6.if you consider forouzan's book of data networking, the answer should be bit 6.then the correct message will be 1100110.

her the parity bits are bit 1,bit 2, bit 4.

now to calculate bit 1=bit1⊕bit3⊕bit5⊕bit7=0⊕1⊕0⊕1=0

again,to calculate bit 2=bit2⊕bit3⊕bit6⊕bit7=1⊕1⊕0⊕1=1

again,to calculate bit 3=bit4⊕bit5⊕bit6⊕bit7=0⊕0⊕0⊕1=1

therefore ,the error is at the position 110 = 6 

please ,think of it mr @jon_snow.


Sudipta Paul

Your answer is correct !

is it correct?
yes it is
0 votes

Yes there is an error in this message at 6-bit position so the correct message is 1100110

answered by (171 points)

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