Q$3($a$)$ A new excess$-3$ representation has been developed which employs $4$ binary

bits to encode a base$-9$ digit $($instead of the typical base$-10).$ Please find an addition example

showing that the carry$-$out from $4-$bit binary addition does not equal to the expected carry$-$out

for the base$-9$ digit.

$($b$)$ You sent the message $m_0{m}_1{m}_2{m}_3=1110$ to your friend using the standard

Hamming code. However, he mistakenly applied XNOR operations throughout all the correction

equations and obtains $c_0{c}_1{c}_2=110.$ Assuming that at most a $1-$bit error has occurred, what was

the $7-$bit message that your friend received?