Hamming code

A single character message was sent in binary, using $7-$bit ASCII encoding with $4$ hamming parity bits. Assume that at most one bit was indeed corrupted during the transmission and the following corrupted binary message was received:

$\backslash [$

$1,1,1,0,1,0,0,1,1,0,1$

$\backslash ]$

Perform Hamming error correction to find the position of the corrupted bit and correct the received message. Note that the "first bit" is the rightmost bit and "last bit" is leftmost bit.

a$)$ Complete the last column "data bits" of the table, filling in received data bits.

Then fill in the last row with received parity bits.

You can fill the rest of the table on paper to work out last "calculated" row of parity bits.

Compare last two rows to work out which bit of the message was corrupted.

b$)$ Enter found position $\backslash ($ n $\backslash )$ of the corrupted bit $(\backslash (1\backslash$leq n $\backslash$leq $11\backslash )),$ counting from the right end of the message:

c$)$ Enter the corrected binary string, preceded with number $9,$ so $12$ digits in total. This is needed to avoid losing digit in your answer if it's zero $($start with $9$ in any case, e$.$g$.$ if your string is $10101101011,$ enter $910101101011).$ Do not use any separator between digits!