$1.$ A $16-$bit system used to represent floating$-$point numbers has the following format:

S Characteristic Fraction

$15141090$

The MSB $($S$)$ is the sign bit $(1$ for $-,0$ for $+).$ Bits $14$ through $10$ are the $5-$bit excess$-15$

representation of the signed exponent. Bits $9$ through $0$ are the $10-$bit fraction. There is a

hidden assumed $1$ to the left of the fraction and the binary point is between the hidden $1$

and the fraction. This system has no representation for Nans, $$infinity or denormalized

values.

a$)(3)$ Show the hex pattern that corresponds to the representation of $-2\mathrm{.}047*103$ using this

floating$-$point format.

b$)(3)$ Show the hex pattern that corresponds to the representation of $+131008\mathrm{.}0$ using this

floating$-$point format