$3$a$.[$Points $5]$Suppose a file has been allocated $50$ disk blocks $($numbered $0.\mathrm{.}49).$ If block $15$ is to be deleted, determine the number of read$/$write operations on blocks assuming: $($i$)$ Contiguous allocation $($ii$)$ Linked allocation $($iii$)$ Indexed allocation $($where the index was already loaded in main memory$)$

$3$b$.[$Points $5]$ Consider a file currently consisting of $50(0.\mathrm{.}49)$ blocks. Assume that the file control block $($and the index block, in the case of indexed allocation$)$ is already in memory. Calculate how many disk I$/$O operations are required for$$contiguous allocation strategy, to add a new block X$.$ Assume that there is no room to grow at$$the beginning but there is room to grow at the end. Also assume that$$the block information to be added is stored in memory.

Block X is to be added at the beginning $($so it becomes the $0$thblock of the file$)$

Block X is to be added in the middle $($so it becomes the $25$thblock of the file$).$

Block X is added at the end $($so it becomes the $50$thblock of the file$).$

$3$c$.[$Points $5]$ Consider a file currently consisting of $50(0.\mathrm{.}49)$ blocks. Assume that the file control block $($and the index block, in the case of indexed allocation$)$ is already in memory. Calculate how many disk I$/$O operations are required for$$linked allocation$$strategy$,$ to add a new block X$.$ Assume that there is no room to grow at$$the beginning but there is room to grow at the end. Also assume that$$the block information to be added is stored in memory.

Block X is to be added at the beginning $($so it becomes the $0$thblock of the file$)$

Block X is to be added in the middle $($so it becomes the $25$thblock of the file$).$

Block X is added at the end $($so it becomes the $50$thblock of the file$).$

$3$d$.[$Points $5]$ Answer the following questions relating to free$-$space management.

$1.$ What is the advantage of managing the free$-$space list as a bit$-$vector as opposed to a linked list?

$2.$ Suppose a disk has $128$ K blocks, each block of $2$ Kbytes, how many blocks are needed for managing a bit$-$vector?