In this problem, we will explore how deepening the pipeline affects performance in two ways: faster clock cycle 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 0.6 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 account 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 mispredictions?