Question $3-$ File System Implementation $(25$ points$)$

$($This question is related to ILO $2$d $-$ describe the principles and techniques used by OS to support persistent data storage$)$

Consider a $64$ GiB thumb$-$drive device with a storage capacity of $64$ GiB that uses the tabular allocation scheme to manage its storage space. In this case, let's assume that the system has a disk block size of $4$ KiB $,$ and each entry in the block allocation table stores a $32-$bit disk block pointer. $[$Note: $\backslash (1\backslash$mathrm$\{$KiB$\}=2^\{10\}\backslash )$ bytes and $\backslash (1\backslash$mathrm$\{$GiB$\}=2^\{30\}\backslash )$ bytes.$]$

$($a$)(10$ points$)$ How many disk blocks on the thumb$-$drive are required to store the block allocation table?

$($b$)(5$ points$)$ Consider the file system uses a data block bitmap for free space management. How many disk blocks are required to store the data block bitmap?

$($c$)(10$ points$)$ Consider a program that has opened a file containing $200$ blocks of data. Assume the block allocation table, data block bitmap and the file's file control block are already loaded to the memory. How many disks I$/$O operations $($read and write$)$ will result when the system removes the $99$th block from the file? Assume after the system updating the metadata, it pushes the update to the disk.