Given $3$ different instruction types $---$ A$,$ B$,$ and C$.$ Each type$-$A$,$ B$,$ and C instruction takes

$30$ns$,20$ns$,$ and $40$ns to complete, respectively. An assembly program has $20$ type$-$A$,30$ type$-$

B$,$ and $50$ type$-$C instructions.

$($a$)$ Assuming a single cycle datapath, how much time is required to execute the above

program?

$($b$)$ Assume a multi$-$cycle datapath with a clock cycle time of $20$ns$.$ How much time $($in nano$-$seconds$)$

is required to complete the execution of this program?