$(5$ points$)$ Assume we are using a simple model for floating$-$point representation similar to the one

used in Chapter $2$ of the textbook which has a $14-$bit format, $5$ bits for the exponent with a bias of

$15($not $16$ as in the textbook$),$ a normalized mantissa of $8$ bits, and a single sign bit.

$($a$)$ Show how the computer would represent the numbers $100\mathrm{.}0$ and $0\mathrm{.}625$ using this representation.

$($b$)$ Show how the computer would add the two floating$-$points numbers in part $($a$)$ by changing one

of the numbers so they are both expressed using the same power of $2.$

$($c$)$ Show how the computer would represent the sum in part $($b$)$ using the given floating point

representation. What decimal value for the sum is the computer actually storing? Explain.