Considerthefloatingpointsystemwith$\backslash$beta $=2,$t$=3,$L$=1,$U$=2.$

$($a$)$ How many floating point numbers are there in this system?

$($b$)$ Find the smallest and largest positive floating point numbers $($in decimal$)$ in this system.

$($c$)$ Find the machine precision $\backslash$eta $($in decimal$)$ of the floating point system if rounding is used.

$($d$)$ Find the machine precision $\backslash$eta $($in decimal$)$ of the floating point system if chopping is used.

$($e$)$ By modifying the Matlab code given in the text, plot the set of all numbers in this floating point system.