Consider a computer where $($Beta $,$ t$,$ L$,$ U$)=(4,5,2,2).$

$($a$)$ What is the largest floating point number in this computer?

$($b$)$ What is the smallest positive floating point number?

$($c$)$ How many floating point numbers are there total? $($Remember $0$ but ignore "non$-$normal$$ numbers.$)$

$($d$)$ What is the value of the rounding unit n$?$

$($e$)$ What is the distance between the smallest positive floating point number and the next smallest floating point number?

$($f$)$ What is the distance between the largest floating point number and the second largest floating point number?