COMPUTER ORGANIZATION AND ASSEMBLY LANGUAGES

HOMEWORK #$1$

A program executes $10$ billion instructions. It executes on an IBM processor that has an average CPI of $1\mathrm{.}2$ and a clock frequency of $3\mathrm{.}2$ GHz$.$ How many seconds does the program take to execute? What is the cycle time of this IBM processor? Assume that an ARM processor takes $4\mathrm{.}5$ seconds to execute the program. What is the speedup provided by the IBM processor, relative to the ARM processor? $(3$ points$)$

Alex builds a $1\mathrm{.}8$ GHz processor where two important programs, A and B$,$ take one second each to execute. Each program has a CPI of $3.$ Elaine is tasked with designing the company's next$-$generation processor. She comes up with an idea that improves the CPI of A to $2\mathrm{.}4$ and the CPI of B to $2\mathrm{.}5.$ But the idea is so complex that the processor can only be implemented with a cycle time of $1$ ns$.$ Does Elaine's new processor out$-$perform Alex$$s processor on program A$?$ How about on program B$?(3$ points$)$

The result of the SPEC CPU$2006$ bzip$2$ benchmark running on an AMD Barcelona has an instruction count of $2\mathrm{.}0$E$12,$ an execution time of $750$ s$.(1$ point each subquestion$)$

Find the CPI if the clock cycle time is $0\mathrm{.}3$ ns$.$

Find the increase in CPU time if the number of instructions of the benchmark is increased by $12\%$ without affecting the CPI.

Find the increase in CPU time if the number of instructions of the benchmark is increased by $12\%$ and the CPI is increased by $10\%.$

Suppose that we are developing a new version of the AMD Barcelona processor with a $5$ 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 $680$ s$.$ Find the new CPI.

This CPI value is larger than obtained in $($a$.)$ as the clock rate was increased. Determine whether the increase in the CPI is similar to that of the clock rate. If they are dissimilar, why?

By how much has the CPU time been reduced?

Consider processors P$1,$ P$2$ and P$3$ executing the same instruction set. P$1$ has a $3\mathrm{.}0$ GHZ clock rate and a CPI of $1\mathrm{.}2.$ P$2$ has a $2\mathrm{.}4$GHZ clock rate and a CPI of $0\mathrm{.}6.$ P$3$ has a $4\mathrm{.}0$GHZ clock rate and a CPI of $2.$

Which processor has the highest performance in terms of $$instructions$/$sec$?($show your work$)(2$ points$)$

If the processors each execute a program in $10$ sec$,$ find the number of cycles $($IC$)$ and the number of instructions. $(2$ points$)$

We are trying to reduce the execution time by $30\%$ by increasing the clock rate. But this will lead to an increase in CPI by $20\%.$ What clock rate do we have to get respectively for all three processors to implement the time reduction? $(2$ points$)$

Is the following statement true or false? Argue for your answer. $2$ points$$ Along with the development of the scale of integrated circuits, the prices have declined monotonically since the $2000$s