b$)$ Consider the use of Hamming codes to send $11-$bit messages. Specifically, consider the message $10011011011.$ First, calculate the Hamming codeword for this message. Second, invert one message bit in that Hamming codeword $($to represent a $1-$bit error$)$ and show how the recipient can use the check bits to correct the inverted bit. $($That is$,$ perform the error correction.$)$