a$)$ What is the $7-$bit encoding of $0010$ when using this code?

b$)$ What is the $7-$bit encoding of $0000$ when using this code?

c$)$ What is the Hamming distance between $7-$bit code words from a$)$ and b$)?$

d$)$ NoNng that $0010$ and $0000$ differ by only $1$ bit and considering your answer to c$),$ explain

why a $1-$bit transmission error can be corrected with a Hamming$(7,4)$ code.