Using a Hamming code and given a $12-$bit message $101110101011,$ determine the following:

$[7]$

a$.$ the number of Hamming bits required $[1]$

b$.$ the total number of transmitted bits $[1]$

c$.$ the value of the Hamming bits $[2]$

d$.$ write out the transmitted message $[1]$

e$.$ illustrate how the Hamming code locates the error if the $3$ rd bit of the transmitted bit

stream changes from a $1$ to a $0.[2]$