to answer the following questions on this page consider an i$-$node file systems with the following pointers :$4$ direct pointers, $3$ signals$-$indirect, $2$ double$-$indirect and $1$ trip$-$indirect. Assume all that internal arrays for indirect pointers have $8$ element. each pointers$/$element needs $4$B$,$ and the block size is $512$B

assuming that the storge is a hard disk drive $($HDD$)$ of size $500$GB$.$ All answers should be in bytes $($if needed, you can use kilo $"$K$",$ mega $"$M$",$ etc$)$;

a$)$what is the maximum file size that system can support?

b$)$what is minimum space overhead for this system?

c$)$ what is maximum space overhead for the system?

for the same system $,$ if we replaced the i$-$node filesystem with FAT filesystem, answer the following:

a$)$ what is maximum the size that this system can support?

b$)$what is the maximum space overhead for the system?

c$)$what is minimum space overhead for the systems?