$2.[20$ points$]$ Let's say that somebody came up with a following format for representation of floating$-$point numbers:

As you can see, the entire representation takes up only $16$ bits. There are seven bits of exponent $($E$),$ which is stored in the "excess$-63"$ format $(63$ is added to the actual exponent e$),$ and $7$ bits of mantissa $($M$).$ Just like in the actual IEEE format, the numbers are stored normalized.

a$)$ Can the decimal number $0\mathrm{.}6$ be completely accurately represented using this format?

b$)$ If not, what are the two best options for representing a number that is close to $0\mathrm{.}6$ using this format? Give the representation and show your work.

c$)$ Which of the two options from b$)$ is better $($i$.$e$.,$ more accurate$)?$ What is the relative error in representing $0\mathrm{.}6$ in this format?