In this exercise, we examine how pipelining affects the clock cycle time of the processor. Problems in this exercise assume that

individual stages of the datapath have the following latencies:

Also, assume that instructions executed by the processor are broken down as follows:

$($a$)$ What is the clock cycle time in a pipelined and non$-$pipelined processor?

$($b$)$ What is the total latency of an $1w$ instruction in a pipelined and non$-$pipelined processor?

$($c$)$ If we can split one stage of the pipelined datapath into two new stages, each with half the latency of the original stage, which

stage would you split and what is the new clock cycle time of the processor?

$($d$)$ Assuming there are no stalls or hazards, what is the utilization of the data memory?

$($e$)$ Assuming there are no stalls or hazards, what is the utilization of the write$-$register port of the "Registers" unit?