$5.$ Disk Storage and Input$/$Output $[30\%]$ Consider a hard disk with $8$ surfaces, $1024$ tracks per surface, $256$ sectors per track and $512-$bytes sectors$.($a$)[5\%]$ Compute the storage capacity of this disk in bytes and in megabytes $(1$ megabyte $=220$ bytes$).($b$)[5\%]$ How many sectors are required to store a file of length $100,500$ bytes? How many bytes are wasted in storing this file? $($c$)[5\%]$ Neglecting CPU time, how long will it take to write the file in $($b$)$ on the disk sequentially $($in consecutive sectors$)$ if the average track$-$to$-$track seek time is $4$ ms $(1$ ms $=103$ second$)$ and the disk rotates at $7200$ rpm$?$ Assume that the head is initially above the first track to be written. $($d$)[5\%]$ Assume that the CPU reads one sector from the disk using interrupt$-$driven I$/$O$,$ with one interrupt per sector. If it takes $2\mathrm{.}5$s $(1$s $=106$ second$)$ to process each interrupt, what percentage of the time will the CPU spend handling I$/$O $($disregard seek time$)?($e$)[5\%]$ Repeat $($d$)$ if the CPU uses DMA, assuming one interrupt per transfer. $($f$)[5\%]$ Explain why in virtually all systems that include DMA modules, DMA access to main memory is given higher priority than CPU access to main memory. If the processor in Question $1($b$)$ is fetching instructions at the rate of $1$ million instructions per second $(1$ MIPS$),$ by how much will the processor be slowed down due to the DMA activity?