Consider three different processors: P$1,$ P$2,$ and P$3$ executing the same instruction set. P$1$ has a $2$ GHz clock rate, P$2$ has a $4$ GHz clock rate and P$3$ has a $3$ GHz clock rate. Which processor has the highest performance measured in instructions per second? Show your calculations. b$.$ If the processors each execute a program in $20$ seconds, then find the number of cycles and the number of instructions. Show your calculations.