Problem $47(30$ points$)$: Assume we are using the simple model for floating$-$point representation as given

in this book $($the representation uses a $14-$bit format, $5$ bits for the exponent with a bias of $15,$ a normalized

mantissa of $8$ bits, and a single sign bit for the number$)$:

a$)$ Show how the computer would represent the numbers $100\mathrm{.}0$ and $0\mathrm{.}25$ using this floating$-$point format.

b$)$ Show how the computer would add the two floating$-$point 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 floatingpoint representation.

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