Problem $1.$ Consider three different processors $P1,P2,$ and $P3,$ executing the same instruction set:

P$1$ has a $3GHz$ clock rate and a CPI of $1\mathrm{.}5$

P$2$ has a $2\mathrm{.}5GHz$ clock rate and a CPI of $1\mathrm{.}0$

P$3$ has a $4\mathrm{.}0GHz$ clock rate and has a CPI of $2\mathrm{.}2$

a$)$ Which processor has the highest performance expressed in instructions per second?

b$)$ If the processors each execute a program in $10$ seconds, find the number of cycles and the number of

instructions.

c$)$ We are trying to reduce the execution time by $30\%$ but this leads to an increase of $20\%$ in the CPI. What

clock rate should we have to get this time reduction?

Problem $2.$ Compilers can have a profound impact on the performance of an application. Assume that for a

program:

compiler A results in a dynamic instruction count of $1\mathrm{.}0E9$ and has an execution time of $1\mathrm{.}1s$

compiler B results in a dynamic instruction count of $1\mathrm{.}2E9$ and an execution time of $1\mathrm{.}5s$

a$)$ Find the average CPI for each program given that the processor has a clock cycle time of $1ns$

b$)$ Assume the compiled programs run on two different processors. If the execution times on the two

processors are the same, how much faster is the clock of the processor running compiler $A^{\text{'}}\text{'}$s code versus the

clock of the processor running compiler B$\text{'}$s code?

c$)$ A new compiler is developed that uses only $6\mathrm{.}0$E$8$ instructions and has an average CPI of $1\mathrm{.}1.$ What is the

speedup of using this new compiler versus using compiler A or B on the original processor?

Please Note: The level of performance expected for students on core competencies and program learning outcomes varies depending on the

course. The numbers at the end of the key assignment name identify the expected level of performance for a specific key assignment. For