what is the data byte encoded in binary Hamming code?

Question

the problem I am presented with is a binary hamming code shown below:

011101000100, what was the data byte encoded and sent from this hamming code?

and the solution is 10101100, could someone explain to me how to approach this problem?

Also posted on CS.SE: http://cs.stackexchange.com/q/50879/755 — D.W., Dec 18 '15 at 00:06

score 0 · Accepted Answer · answered Dec 18 '15 at 02:43

You will need to calculate the parity bits of data, as follows: $\dot0\dot11\dot1010\dot00100$

p1(0)(10000) 1 error because number of 1s is odd
p2(1)(11010) 
p4(0)(0100)
p8(0)(0100) 1 error
1 + 8 = 9, this is the bit where you have the error

now we replace the 0 in the 9th bit with 1, and after you take out the parity bits, you are then left with $10101100$

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