Problem $2.(12$ points$)$:

Data representation. Consider the following two $9-$bit floating point representations based on the IEEE

floating point format.

Format A

There is one sign bit.

There are $k=5$ exponent bits. The exponent bias is $15.$

There are $n=3$ fraction bits.

Format B

There is one sign bit.

There are $k=4$ exponent bits. The exponent bias is $7.$

There are $n=4$ fraction bits.

Numeric values are encoded in both of these formats as a value of the form $V=(-1{)}^{S}M{2}^E,$ where

$S$ is the sign bit, $E$ is exponent after biasing, and $M$ is the significand value. The fraction bits encode the

significand value $M$ using either a denormalized $($exponent field $0)$ or a normalized representation $($exponent

field nonzero$).$

Below, you are given some bit patterns in Format A$,$ and your task is to convert them to the closest value in

Format B$.$ If rounding is necessary you should round toward $+.$ In addition, give the values of numbers

given by the Format A and Format B bit patterns. Give these as whole numbers $($e$.$g$.,17)$ or as fractions

$($e$.$g$.,\frac{17}{64}$ or $\frac{17}{2^6}).$