Q$12$marks Consider a hard drive $($rotating disk$)$ with $4$ platters. Suppose both surfaces of platters are used for recording. $($a$)$ How many heads does the hard drive have? $($b$)$ How many tracks are per cylinder? Q$23$marks Modernhigh$-$capacity hard drives use a technique known as multiple zone recording, where the set of cylinders is partitioned into disjoint subsets known as recording zones. Each zone consists of a contiguous collection of cylinders. Each track in each cylinder in a zone has the same number of sectors$,$ which is determined by the number of sectors that can be packed into the innermost track of the zone. Suppose both surfaces of platters are used for data recording. What is the capacity of a hard drive with the following parameters? $($write your answer in gigabytes; $1$GB $=109$ bytes$)($a$)$ number of platters $=8($b$)$ number of bytes per sector $=512($c$)$ number of zones $=2($d$)$ number of cylinders per zone $1=8,000($e$)$ number of cylinders per zone $2=10,000($f$)$ number of sectors per track for zone $1=800($g$)$ number of sectors per track for zone $2=400$ Q$34$marks Estimate the average time $($in ms$)$ to access a sector on the following disk: Parameter Value Rotational rate Tavg seek $12,000$ RPM $5$ms Average # sectors$/$track $500$ Q$46$marks Suppose that a $2$MiB file consisting of $512-$byte logical blocks is stored on a disk drive with the following characteristics: Parameter Value Rotational rate Tavg seek $12,000$ RPM $6$ms Average # sectors$/$track $1000$ Surfaces $8$ Sector size $512$ bytes $($a$)$ Best case: Estimate the optimal time $($in ms$)$ required to read the file over all possible mappings of logical blocks to disk sectors$.$ Justify your answer. $($b$)$ Randomcase: Estimate the time $($in ms$)$ required to read the file if blocks are mapped randomly to disk sectors$.$ Justify your answer. Remark: Assume that the hard disk drive $($HDD$)$ cannot access data in parallel through its multiple heads. Before RAID systems become popular, some modern hard disk drives could access data in parallel through multiple heads. In those HDDs$,$ the heads needed to be aligned with each other very accurately which was difficult because of various reasons including vibration, and mechanical imperfections. As track density increased, alignment became even more difficult, and the advent of RAID technology practically eliminated the need for those high performance HDDs