$1.$ Calculate timer parameters for a down$-$counting timer with a load option. $(20$ points$)$

a$.$ For a timer clocked at $24$MHz with a $24-$bit up$-$counter, how long, in milliseconds, will it take $($from reset: count$=0)$ to reach the load value of $0$x$012$B$45?$

b$.$ For a timer clocked at $16$MHz with a $16-$bit down$-$counter, what value should be loaded into the timer so that it will take $2$msec to reach $0?$

c$.$ For a timer clocked at $32$MHz$,$ if we wanted $750$msec, how many bits must the counter have $($minimum$)$ and what load value would be needed?

d$.$ For a $12-$bit down$-$counting timer clocked at $32$kHz$,$ if the count starts at $0$xE$0$E$,$ what will the count be after $12$msec?

e$.$ If we want the tc output to pulse every $0\mathrm{.}5$ sec$,$ what start values should be loaded into a $32-$bit down$-$counting timer assuming clk $=18$MHz$?$ Assume the timer counter will wrap back to the load$/$start value rather than to its max value $($which is standard operation$).$