$1\mathrm{.}5[4]<1\mathrm{.}6>$ Consider three different processors P$1,$ P$2,$ and P$3$ executing the same

instruction set. P$1$ has a $3$ GHz clock rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}5$ GHz clock rate

and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}0$ GHz clock rate and has a CPI of $2\mathrm{.}2.$

a$.$ Which processor has the highest performance expr essed 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?

$1\mathrm{.}8[15]<1\mathrm{.}6>$ Compilers can have a profound impact on the performance of an

application. A ssume that for a program, compiler A results in a d ynamic instruction

count of $1\mathrm{.}0$E$9$ and has an execution time of $1\mathrm{.}1$ s$,$ while compiler B results in a

d yn amic instruction count of $1\mathrm{.}2$E$9$ and an execution time of $1\mathrm{.}5$ s$.$

a$.$ Find the average CPI for each program given that the processor has a clock cy cle

time of $1$ ns$.$

b $.$ Assume the compiled progr ams 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$\text{'}$s code versus the clock of the processor running

compiler B$\text{'}$s code?

c$.$ A new compiler is d eveloped that u ses only $6.$oES instructions and h as an average

CPI of $1.1.$ What is the speedup of u sing this new compiler versus u sing

compiler A or B on the original processor?

$1\mathrm{.}10$ Assume for arithmetic, load$/$store$,$ and branch instructions, a processor has CPis

of $1,12,$ and $5,$ respectively. Also assume that on a single processor a program

requires the execution of $2\mathrm{.}569$ arithmetic instructions, $1\mathrm{.}289$ load$/$store

instructions, and $256$ million branch instructions. Assume that each processor has a

$2$ GHz clock frequency.

Assume that, as the program is parallelized to run over multiple cores, the number of

arithmetic and load$/$store instructions per processor is divided by $0\mathrm{.}7$ x p $($where pis

the number of processors$)$ but the number of branch instructions per processor

remains the same.

$1\mathrm{.}10\mathrm{.}1[5]<1\mathrm{.}7>$ Find the total execution time for this program on $1,2,4,$ and $8$

processors, and show the relative speedup of the $2,4,$ and $8$ processor result

relative to the single processor result.

$1\mathrm{.}10\mathrm{.}2[10]<1\mathrm{.}6,1\mathrm{.}8>$ If the CPI of the arithmetic instructions was doubled,

what would the impact be on the execution time of the program on $1,2,4,$ or $8$

processors?

$1\mathrm{.}10\mathrm{.}3[10]<1\mathrm{.}6,1\mathrm{.}8>$ To what should the CPI of load$/$store instructions be

reduced in order for a single processor to match the performance of four

processors using the original CPI values?