There are five classes of instructions $($A$,$ B$,$ C$,$ D and E$)$ in the instruction set. The processor has a clock rate of $4$ GHz $.$ The following table shows the CPI and the percentage of instructions executed by each class for a given program.

$($a$)$ Compute the average CPI.

$($b$)$ If $10$ billion instructions were executed, what is the execution time in seconds?

$($c$)$ What percent of the execution time is used by each class of instructions?

$($d$)$ When you run the program, it takes $15$ seconds to complete. What percentage of time the program is running on the CPU, and the percentage of time it is waiting?

$($e$)$ A newer processor reduces the CPI of class D instructions to just $1$ cycle and of class E to just $2$ cycles. It uses a faster $5$ GHz clock. What is the new average CPI and the speedup of running the program on the newer processor?