Problem $1$ Pipeline Control Hazard $($Chapter $4)$

The importance of having a good branch predictor depends on how often conditional branches are executed. Together with branch predictor accuracy, this will determine how much time is spent stalling due to mis$-$predicted branches. Assume we have the following breakdown of dynamic instructions.

Also, assume the accuracies of the three different branch predictors are as follows:

If the branch target address will be available the same cycle the branch condition is resolved, i$.$e$.$ in EX stage $($different from Lecture slides$).$ So$,$ there is a $2-$cycle penalty for a branch mis$-$prediction. Please answer the following $5$ questions.

A$.$ Stall cycles due to mis$-$predicted branches increase the CPI. What is the extra CPI due to mis$-$predicted branches with the always$-$taken predictor? Assume branch outcomes are determined in EX stage, and there is no data hazard.

B$.$ Repeat the above question with an always$-$not$-$taken predictor.

C$.$ Repeat the above question with a $2-$bit predictor.

D$.$ With the $2-$bit predictor, what speedup would be achieved if we could convert half of the branch instructions in a way that replaces a branch instruction with an ALU instruction? Assume that correctly and incorrectly predicted instructions have the same chance of being replaced.

E$.$ With the $2-$bit predictor, what speedup would be achieved if we could convert half of the branch instructions in a way that replaced each branch instruction with $2$ ALU instructions? Assume that correctly and incorrectly predicted branch instructions have the same chance of being replaced.