Problem $3$

Consider a hypothetical floating point system in base$-2$ that uses $11-$bit words. The system stores $1$ digit for the sign, $k=5$ digits for the exponent, and $t=5$ digits for the fraction portion of the mantissa. Aside from the number of digits $($bits$),$ 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 sig figs$)$

Please, explain the solutions as well!