$2...$A particular system is controlled by an operator through commands entered from a keyboard. The average number of commands entered in an $12-$hour interval is $400012+2=4$ Marks$)$

a$.$Suppose the processor scans the keyboard every $400$ ms$.$ How many times will the keyboard be checked in an $12-$hour period?

b$.$ By what fraction would the number of processor visits to the keyboard be reduced if interrupt$-$driven I$/$O were used.