A Floating Point Number System $($FPNS$)$ is defined by a tuple FPNS $(\backslash$beta $,$ t$,$ pmin, pmax$)$

where $\backslash$beta is the base, t is the precision, and pmin, pmax are the minimum and maximum

exponents, respectively. Use the system FPNS $(16,3,4,4)$ for the following questions.

You can provide your answer in base $16.$

$($a$)$ What is the largest value in the system?

$($b$)$ What the smallest positive number in the system?

$($c$)$ What is the largest number less than one in the system?

$($d$)$ What is the smallest number greater than one in the system?

$($e$)$ What is the size of the gap between $409610$ and the next larger value in the system?