Assume a program requires the execution of $60\backslash$times $106$ FP instructions, $120\backslash$times $106$ INT instructions, $60\backslash$times $106$ L$/$S instructions, and $16\backslash$times $106$ branch instructions. The CPI for each type of instruction is $1,1,4,$ and $2,$ respectively. Assume that the processor has a $2$ GHz clock rate.$($a$)$ By how much must we improve the CPI of FP instructions if we want the program to run two times faster?$($b$)$ By how much must we improve the CPI of L$/$S instructions if we want the program to run two times faster?$($c$)$ By how much is the execution time of the program improved if the CPI of INT and FP instructions is reduced by $50\%$ and the CPI of L$/$S and Branch is reduced by $25\%?2.$ When a program is adapted to run on multiple processors in a multiprocessor system, the execution time on each processor is comprised of computing time and the overhead time required for locked critical sections and$/$or to send data from one processor to another.Assume a program requires t $=200$ s of execution time on one processor. When running p processors, each processor requires t$/$p s$,$ as well as an additional $10$ s of overhead, irrespective of the number of processors. Compute the per$-$processor execution time for $2,4,8,16,32,64$ processors. For each case, list the corresponding speedup relative to a single processor and the ratio between actual speedup versus ideal speedup $($speedup if there was no overhead$)\mathrm{.}3.$ Assume for arithmetic, load$/$store$,$ and branch instructions, a processor has CPIs of $2,10,$ and $5,$ respectively. Also assume that on a single processor, a program requires the execution of $2\mathrm{.}56$E$9$ arithmetic instructions, $1\mathrm{.}28$E$9$ load$/$store instructions, and $128$ 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 $0\mathrm{.}7\backslash$times p $($where p is the number of processors$)$ but the number of branch instructions per processor remains the same.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 $8$ processors result relative to the single processor result.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? $4.$ One challenge for architects is that the design created today will require several years of implementation, verification, and testing before appearing on the market. This means that the architect must project what the technology will be like several years in advance. Sometimes, this is difficult to do$.$a$.$ According to the trend in device scaling historically observed by Moores Law, the number of transistors on a chip in $2025$ should be how many times the number in $2015?[$assume # Transistors double every $2$ years$]$b$.$ The increase in performance once mirrored this trend. Had performance continued to climb at the same rate as in the $1990$s$,$ approximately what performance would chips have over the VAX$-11/780$ in $2025?[$assume performance increases $52\%$ every year$]5.$ Consider the following two processors. P$1$ has a clock rate of $4$GHz$,$ average CPI of $0\mathrm{.}9,$ and requires the execution of $5\mathrm{.}0$E$9$ instructions. P$2$ has a clock rate of $3$GHz$,$ an average CPI of $0\mathrm{.}75,$ and requires the execution of $1\mathrm{.}0$E$9$ instructions.a$.$ One usual fallacy is to consider the computer with the largest clock rate as having the highest performance. Check if this is true for P$1$ and P$2.$b$.$ Another fallacy is to consider that the processor executing the largest number of instructions will need a larger CPU time. Considering that processor P$1$ is executing a sequence of $1\mathrm{.}0$E$9$ instructions and that the CPI of processors P$1$ and P$2$ do not change, determine the number of instructions that P$2$ can execute in the same time that P$1$ needs to execute $1\mathrm{.}0$E$9$ instructions.c$.$ A common fallacy is to use MIPS $($millions of instructions per second$)$ to compare the performance of two different processors, and consider that the processor with the largest MIPS has the largest performance. Check if this is true for P$1$ and P$2.$