If a computer uses only ONE $8$ bits binary register to represent a number using floating point representation $(1$ bit for sign bit, $2$ bits for exponent, and $5$ bits for the significand$)(10$ points$)$

$($a$).$ What should be a good bias for the exponent?

$($b$).$ What are the largest and smallest positive numbers this register ean hold with the bias?

$($c$).$ What are the largest and smallest negative numbers this register ean hold with the bias?

$($d$).$ How many numbers can be represented using this register?

$($e$)$ How is number $2\mathrm{.}33$ stored in the register? $($show work$)$