$1.$ A certain program contains $2,480,000$ instructions. Each instruction is executed exactly

once on a processor running at a $4$ GHz clock rate. The program contains no branch or jump

instructions. Twenty$-$two percent of the instructions are lw instructions, twelve percent of

the instructions are sw instructions, and all of the remaining instructions are R$-$type

instructions. Recall that our MIPS pipeline system is an example of a scalar pipeline since

no more than one instruction at a time can occupy any stage. Answer the following

questions about this program.

a$)(5)$ If the first instruction to enter the empty scalar pipeline is an R$-$type instruction,

what is the maximum number of nano$-$seconds required for that R$-$type instruction to

complete all five pipeline stages if the clock rate is $4$ GHz$?$

b$)(5)$ After the first R$-$type instruction completes the write$-$back stage, what is the

maximum throughput for the pipeline? Recall that the throughput is the number of

instructions per second the pipeline completes