In this problem, we will explore how deepening the pipeline affects

performance in two ways: faster clock cycles and increased stalls due to data and control hazards.

Assume that the original machine is a $5-$stage pipeline with a $1$ns clock cycle. The second machine is

a $12-$stage pipeline with a $0\mathrm{.}6$ns clock cycle. The $5-$stage pipeline experiences a stall due to a data

hazard every five instructions, whereas the $12-$stage pipeline experiences three stalls every eight

instructions. In addition, branches constitute $20\%$ of the instructions, and the misprediction rate

for both machines is $5\%.$

a$).$ What is the speedup of the $12-$stage pipeline over the $5-$stage pipeline, taking into only data hazards?

b$).$ If the branch mispredict penalty for the first machine is $2$ cycles but the second machine is $5$ cycles,

what are the CPIs of each, taking into account the stalls due to branch misprediction