In the classes, we discussed three forms of floating number representations as given below,

$(1)$ Standard$/$General Form, $(2)$ Normalized Form, $(3)$ Denormalized Form.

Now, let$$s take,

$\backslash$beta $=2,$ m $=3,$ emin $=-2$ and emax $=3.$ Based on these, answer the following:

$($a$)(2$ marks$)$ What are the maximum$/$largest numbers that can be stored in the system by these three forms defined above? $($express your answer in decimal values$)$

$($b$)(2$ marks$)$ What are the non$-$negative minimum$/$smallest numbers that can be stored in the system by the denormalized form? $($express your answer in decimal values$)$

$($c$)(2$ marks$)$ How many numbers $($both non$-$negative and negative$)$ can be represented in the above mentioned system using the general form? Explain your answer.

$($d$)(4$ marks$)$ Find all the decimal numbers for e $=3$ and e $=2$ in denormalized form, plot them on a real line and prove that all the numbers are not equally spaced. Write the equally spaced sets for the number line you drew.