Question $2$: File System $($Max Mark: $15/100)$

A simple file system has the same structure as the one in Task $10\mathrm{.}2.$ First, there is an

inode bitmap, which marks whether each corresponding inode is allocated $(1)$ or free $(0).$

There are $16$ inodes. Each allocated inode has contents consisting of three fields. The

first field is either f $($file$)$ or d $($directory$).$ The second field a either points to a single data

block or is $-1$ which indicates that the files is empty. Note that in this limited file system,

each file or directory can only occupy a single data block. The third field is a reference

count for files. For directories, it indicates the number of directories within this directory.

Task: Answer the questions in each of the following cases.

$(1)$ Consider the state of the file system below:

inode bitmap $1000100110010001$

inodes $[$d a:$0$ r:$4][][][][$f a:$-1$ r:$1][][][$d a:$15$ r:$2]$

$[$d a:$22$ r:$2][][][$f a:$-1$ r:$3][][][][$f a:$-1$ r:$1]$

data bitmap $100000000000000100000010$

data $[(.,0)(..,0)($m$,7)($a$,8)($g$,11)][][][][][][][]$

$[][][][][][][][(.,7)(..,0)($m$,15)($e$,11)]$

$[][][][][][][(.,8)(..,0)($r$,4)($w$,11)][]$

Question: List all the files and directories that are currently in this file system.