Chapter $31.$ The IBM $360$ had a scheme of locking $2-$KB blocks by assigning each one a $4-$bit key and having the CPU compare the key on every memory reference to the $4-$bit key in thePSW. Name two drawbacks of this scheme not mentioned in the text$\mathrm{.}2.$ Consider a swapping system in which memory consists of the following hole sizes in memory order: $10$ MB$,4$ MB$,20$ MB$,18$ MB$,7$ MB$,9$ MB$,12$ MB$,$ and $15$ MB$.$ Which hole is taken for successive segment requests of $($a$)12$ MB $($b$)10$ MB $($c$)9$ MB for first fit? Now repeat the question for best fit, worst fit, and next fit$\mathrm{.}3.$ What is the difference between a physical address and a virtual address?$4.$ If an instruction takes $1$ uses and a page fault takes an additional n uses, give a formula for the effective instruction time if page faults occur every k instructions$5.$ Suppose that a machine has $38-$bit virtual addresses and $32-$bit physical addresses. $($a$)$What is the main advantage of a multilevel page table over a single$-$level one? $($b$)$ With a two$-$level page table, $16-$KB pages, and $4-$byte entries, how many bits should be allocated for the top$-$level page table field and how many for the next$-$ level page table field?Chapter $41.$ Give five different path names for the file $/$etc$/$passwd$,($Hint: Think about the dires tory entries $""$ and $"".).$and data segments. Why do you think a very specific number was chosen for executable files, whereas other file types had a more$-$or$-$less random magic number as the first word?$3.$ Contiguous allocation of files leads to disk fragmentation, as mentioned in the text, because some space in the last disk block will be wasted in files whose length is not anintegral number of blocks. Is this internal fragmentation or external fragmentation? Make an analogy with something discussed in the previous chapter$\mathrm{.}4.$ One way to use contiguous allocation of the disk and not suffer from holes is to compact the disk every time a file is removed. Since all files are contiguous, copying a file requires a seek and rotational delay to read the file, followed by the transfer at full speed.Writing the file back requires the same work. Assuming a seek time of $5$ msec, a rotational delay of $4$ msec, a transfer rate of $80$ MB$/$sec$,$ and an average file size of $8$ KB$,$ how long does it take to read a file into main memory and then write it back to the disk at a new location? Using these numbers, how long would it take to compact half of a $16-$GB disk?$5.$ Consider a $4-$ TB disk that uses $4-$KB blocks and the free$-$list method. How many block addresses can be stored in one block?