Consider two different implementations of the same instruction set architecture. The instructions can be divided into four classes according to their CPI $($classes A$,$ B$,$ C$,$ and D$).$ P$1$ with a clock rate of $3$ GHz and CPIs of $1,2,3,$ and $3,$ and $P2$ with a clock rate of $2GHz$ and CPIs of $2,2,2,$ and $2.$ Given a program with a dynamic instruction count of ${10}^3$ instructions divided into classes as follows: $50\%$ class A$,20\%$ class B$,20\%$ class C$,$ and $10\%$ class D$,$

$($a$)$ What is the global CPI for each implementation?

$($a$)$ Which is faster: P$1$ or P$2?$