Q$5.$ A program being executed on a processor has the following instructions mix:

$($i$)$ Compute the average clock cycles per instruction.

$($ii$)$ A designer wants to improve the performance. He designs a new execution unit that makes $80\%$ of ALU operations take only $1$ cycle to execute. Executing the other $20\%$ of ALU operations will still take $3$ cycles. The designer also wants to improve the execution of the memory access instructions. He does it so that $95\%$ of the load instructions take only $2$ cycles to execute, while the remaining $5\%$ of the load instructions take $8$ cycles to execute per load.

He also improves the store instructions so that each instruction takes $2$ cycles to execute.

Compute the new average cycles per instruction.

$($iii$)$ What is the speedup factor by which the performance has improved in part $($ii$)?$

$($iv$)$ The designer decides to improve the clock speed in such a way to triple the overall performance of the original CPU specified in part $($i$).$ What factor should the clock rate be improved if the designer uses the design specified in part $($ii$)?$