Consider the $3$rd$,4$th$,$ and $6$th digits of your student ID composed of seven digits. Convert it to binary format $($each digit is represented by a maximum of $4$bits$).$ For example, $1087365$ is simplified to $876$ and then converted to $100001110110.$ If any of the three digits is equal to zero, then you need converted to number $9.$ Assume now that we want to send your simplified student ID while being able to detect and correct single bit errors.

$1\mathrm{.}1)(0\mathrm{.}25$ mark$)$ Using two$-$dimensional parity check show what will be transmitted using datawords of size $4$bits.

$1\mathrm{.}2)(0\mathrm{.}5$ mark$)$ Using the hamming code show what would be the codeword that corresponds to your simplified binary student ID$.$ Dataword size is $12$bits.

$1\mathrm{.}3)(0\mathrm{.}5$ mark$)$ Assume that a single bit error occurred and corrupted the $11$th bit. Show that the receiver of such corrupted codeword will be able to detect and correct the error when using the hamming code.