$3.[0\mathrm{.}2$ marks$]$ Consider a paged logical address space $($composed of $32$ pages of $2$ Kbytes each$)$ mapped into a $1-$Mbyte physical memory space.

a$.$ What is the format of the processor's logical address?

b$.$ What is the length and width of the page table $($disregarding all the control bits$)?$

c$.$ What is the effect on the page table if the physical memory space is reduced by half? Assume that the number of page entries and page size stay the same.

$4.[0\mathrm{.}5$ marks$]$ Explain, in detail, what a write operation must do$.$ Consider the case of a file opened for APPEND, in a file system using a hierarchical directory structure.

$5.$ File System

a$)[0\mathrm{.}5$ marks$]($from Silberschatz$)$ Consider a file system that uses inodes to represent files. Disk blocks are $8$ Kb in size, and a pointer to a disk block requires $4$ bytes. This file system has $12$ direct disk blocks, as well as single, double, and triple indirect disk blocks. What is the maximum size of a file that can be stored in this file system?

b$)[0\mathrm{.}5$ marks$]$ Explain what you can do in case $($a$)$ if you need to store a file that is larger than the maximum size computed. Give an example showing how you can define a larger file, and what the size of that file would be$.$