$3.$ The results of the SPEC CPU$2006$ bzip$2$ benchmark running on an AMD Barcelona has an

instruction count of $2\mathrm{.}389$E$12,$ an execution time of $750$ s$.(1$ point each subquestion$)$

a$.$ Find the CPI if the clock cycle time is $0\mathrm{.}333$ ns$.$

b$.$ Find the increase in CPU time if the number of instructions of the benchmark is

increased by $10\%$ without affecting the CPI.

c$.$ Find the increase in CPU time if the number of instructions of the benchmark is

increased by $10\%$ and the CPI is increased by $5\%.$

d$.$ Suppose that we are developing a new version of the AMD Barcelona processor

with a $4$ GHz clock rate. We have added some additional instructions to the

instruction set in such a way that the number of instructions has been reduced

by $15\%.$ The execution time is reduced to $700$ s$.$ Find the new CPI.

e$.$ This CPI value is larger than obtained in a$.$ as the clock rate was increased from $3$

GHz to $4$ GHz$.$ Determine whether the increase in the CPI is similar to that of the

clock rate. If they are dissimilar, why?

f$.$ By how much has the CPU time been reduced?