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

$($a$)$ Which of the following numbers are floating point numbers in this computer? Select all that apply and explain briefly.

$($i$)$ one sixty$-$fourth

$($ii$)$ three sixteenths

$($iii$)$ one third

$($iv$)$ seven

$($v$)$ two hundred and fifty$-$six

$($b$)($i$)$

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

What is the largest floating point number in this computer?

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

$($iv$)$ What is the value of the rounding unit $\backslash$eta $?$

$($c$)$ What is the distance between the smallest positive floating point number and the

next smallest floating point number?

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

floating point number?