RISC V A pipeline having $12$ stages executes a program having $3000$ instructions.

Branch operations are $20\%$ of the total number of instructions, and $60\%$ of the branches are

taken. The penalty for each taken branch is $5$ cycles. Furthermore $30\%$ of the instructions

are load operations of which $40\%$ incur a load$-$use data hazard $($which can not be resolved by

forwarding$)$ and results in $1$ stall cycle.

a$)$ Evaluate the average CPI of the processor.

b$)$ Assume that a branch prediction unit is introduced to improve the average CPI. What

accuracy of the branch prediction unit will improve the average CPI to $1\mathrm{.}5.$