I am trying to answer this hamming code error detection and correction problem, and I am not sure if I'm wrong or if the given is wrong. Can anybody help? Note: I'm studying this on my own (yt vids) since our professor refuses actually to teach things, so I might have interpreted things differently.
Here is the given:
Suppose we are working with an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 7. We have already calculated that we need 4 check bits, and the length of all code words will be 11. Code words are created according to the Hamming algorithm presented in the text. We now receive the following code word: 10101010110. Assuming odd parity, is this a legal code word? If not, according to our error-correcting code, where is the error?
My initial solution is to check the parity.*assuming odd parity, if there are odd bits of 1, it is equal to 0, and if even, it is equal to 1
Parity1 (11, 9, 7, 5, 3, 1) = 111110 (odd) = 0
Parity2 (11, 10, 7, 6, 3, 2) = 101011 (even) = 1
Parity4 (7, 6, 5, 4) = 1010 (even) = 1
Parity8 (11, 10, 9, 8) = 1010 (even) = 1
1110 = 14 in decimal, but the size of the word is only 11
I'm still new to the topic, and I can't wrap my head around it. I hope somebody helps. Thanks