Question $2$ only please $(25$ points$)[$Float Point Design$]$ In a hypothetical $5-$bit floating point format, $3$ leading bits

are used for exponent, $E,$ in two's compliment format and the two remaining bits are for the

fraction $F,$ where the number is determined using $x=1.F{2}^E.$ Answer the following

questions:

$($a$)$ What is the decimal value of the five bits set to $01101?$

$($b$)$ What is the decimal value of the five bits set to $10010?$

$($c$)$ What is the range of this format?

$($d$)$ How would a $7$ get represented in these five bits?

$($e$)$ How would $0\mathrm{.}375$ get represented?

$($f$)$ How many distinct numbers can be represented in this format?

$(15$ points$)[$Float Point Design$]$ From problem $1,$ if we change how a number is determined

using the following functions, what is the new range, and how many distinct numbers can be

represented?

$($a$)x=F\mathrm{.}02^E.$

$($b$)x=0.F{2}^E.$

$($c$)x=F\mathrm{.}12^E.$