$[20\%]$ Consider a computer with a $64-$entry TLB in its main processor. The computer has a hard disk spinning at $5400$ RPM and holding $40$ sectors per track with a sector size of $512$ bytes. In addition, the access latency time for the hard drive is $10$ milliseconds, and the seek time is $30$ milliseconds.

$(1)$ Calculate TLB reach when the computer supports memory page sizes of $1$ KB and $4$ KB$,$ respectively.

$(2)$ Compute the data transfer rate of the hard disk in KB$/$s$.$

$(3)$ Estimate the I$/$O times when page faults occur; give your I$/$O times in milliseconds for handling the page fault of a $1-$KB page and a $4-$KB page, respectively.

$(4)$ We assume that the data transfer time of the hard disk is proportional to the page size. What are the I$/$O times to transfer the same amount of data $($i$.$e$.,4$KB data$)$ with $1-$KB and $4-$KB pages, respectively? In such a case, if we want to minimize the I$/$O time on the computer, which page size $(1$ KB or $4$KB$)$ is desired?