$4.(20$ points$)$ File System

Consider a file system that has the following description:

$-$ The hard disk is divided into $2048-$byte blocks.

$-$ As shown in the figure, a file is stored in hard disk using indexed allocation. A File Control Block $($FCB$)$ contains:

$-12$ data block pointers, each of which is $4$ bytes and each of which points to a disk block.

$-$ ONE single indirect pointer, which points to a disk block that contains data block pointers.

$-$ ONE double indirect pointer, which points to a block of pointers that point to other blocks of pointers that then point to data.

$-$ The FCB also contains a user id $(2$ bytes$),3$ timestamps $(4$ bytes each$),1$ protection bits $(2$ bytes$),$ a reference count $(3$ bytes$),$ and a size block count $(4$ bytes$).$

a$)(10$ points$)$ What is the maximum file size supported by this file system? Briefly explain.

b$)(10$ points$)$ Consider file $\backslash ($ A $\backslash )$ with size $10$ KB $,$ file $\backslash ($ B $\backslash )$ with size $1$ MB $,$ and file $\backslash ($ C $\backslash )$ with size $250$ MB $.$ Does the file system take the same amount of time to obtain the index of the last block of $\backslash ($ A$,$ B$,$ C $\backslash )$ and why?