Consider a hypothetical floating point system in base$-2$ that uses $9-$bit words. The system stores $1$ digit for

the sign, $k=4$ digits for the exponent, and $t=4$ digits for the fraction portion of the mantissa. Aside

from the number of digits, this floating point system follows all rules of the IEEE $754$ standard. Answer the

following questions about the hypothetical floating point system:

$($a$)$ What are the lower and upper bounds, $L$ and $U,$ on the exponent for normalized numbers?

$($b$)$ What is the approximate value of the largest positive normalized number that can be represented by

this floating point system? $($report your answer in base$-10$ with three significant digits$)$

$($c$)$ What is the machine precision? $($report your answer in base$-10$ with three significant digits$)$