Computer organization
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Computer Organization. Lab 1 Soufiane berouel. Formulas to Remember. CPU Time = CPU Clock Cycles x Clock Cycle Time CPU Clock Cycles = Instruction Count x Cycles per Instruction Clock Cycle Time = 1 / Clock Cycle Rate Amdahl’s Law

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Computer organization

Computer Organization

Lab 1

Soufiane berouel


Formulas to remember

Formulas to Remember

  • CPU Time = CPU ClockCycles x ClockCycle Time

  • CPU Clock Cycles = Instruction Count x Cycles per Instruction

  • Clock Cycle Time = 1 / Clock Cycle Rate

  • Amdahl’s Law

    • Overall Speedup= 1 / [(1 – ∑ FEi) + ∑ (FEi/ SEi)]

    • FE is the proportion affected, SE is the speed up for the specific proportion


Exercise 1

Exercise 1

  • For a color display using 8 bits for each primary color (R, G, B) per pixel and with a resolution of 1280 x 800 pixels, what should be the size (in bytes) of the frame buffer to store a frame?


Exercise 1 sol

Exercise 1 (sol)

  • Each frame requires 1280 x 800 x 3 = 3072000 ~ 3 Mbytes


Exercise 2

Exercise 2

  • Consider 3 processors P1, P2 and P3 with clock rates and CPI given below, are running the same program:

    clock rate CPI

    P1 2 GHz 1.5

    P2 1.5 GHz 1.0

    P3 3 GHz 2.5

  • Which processor will have the best performance?


Exercise 2 sol

Exercise 2 (sol)

  • Suppose the program has N instructions.

  • Time taken to execute on P1 is = 1.5 N / (2 x 109) = 0.75 N x 10-9

  • Time taken to execute on P2 is = N/ (1.5 x 109) = 0.66 N x 10-9

  • Time taken to execute on P3 is = 2.5 N/ (3 x 109) = 0.83 N x 10-9

  • P2 has the best performance (since it takes the least time to execute).


Exercise 3

Exercise 3

  • Consider 3 processors P1, P2 and P3 with same instruction set with clock rates and CPI given below:

    clock rate CPI

    P1 2 GHz 1.5

    P2 1.5 GHz 1.0

    P3 3 GHz 2.5

  • If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.


Exercise 3 sol

Exercise 3 (sol)

  • For P1

    • 10 (execution time) = 1.5 (CPI) x N1/ (2 x 109)

    • So N1 (number of instructions) = 1.33 x 1010

    • Number of Cycles = 1.5 x N1 = 2 x 1010

  • …Do the same for P2 and P3


Exercise 4

Exercise 4

  • Given below are the number of instructions of a program:

    arithmetic store load branch

    500 50 100 50

  • Assuming the instructions take 1, 5, 5 and 2 cycles, what is the execution time in a 2 GHz processor?


Exercise 4 sol

Exercise 4 (sol)

  • Execution time = cycle time x CPI x no. of inst

    • Cycle time = 1/(2 x 109)

    • CPI = (500 x 1 + 50 x 5 + 100 x 5 + 50 x 2) / (500 + 50 + 100 + 50)

    • Thus, Execution Time = 1350 / 700 x 700 / (2 x 10-9)

  • So the Execution time = 675 x 10-9 sec


Exercise 5

Exercise 5

  • Compilers have a profound impact on the performance of an application on a given processor. This problem will explore the impact compilers have on execution time:

    compiler A compiler B

    no instructions exec. Time no. instructions exec. Time

    a) 1.0 x 109 1 s 1.2 x 109 1.4 s

    b) 1.4 x 109 0.8 s 1.2 x 109 0.7 s

  • Find the average CPI for programs a and b, on different compilers, given that the processor has a cycle time of 1 ns.


Exercise 5 sol

Exercise 5 (sol)

  • Execution Time = CPI x cycle time x no. of inst

    • cycle time = 1ns = 10-9 s

  • For program a on Compiler A

    • CPI = 1 / (10-9 x 109 ) = 1

  • For program a on Compiler B

    • CPI = 1.4 / (10-9 x 1.2 x 109 ) = 1.667

  • Do the same for program b…


  • Exercise 6 a

    Exercise 6 - a

    • Three enhancements with the following speedups are proposed for a new architecture:

      Speedup1 = 30

      Speedup2 = 20

      Speedup3 = 10

    • Only one enhancement is usable at a time.

      a. If enhancements 1 and 2 are each usable for 30% of the time, what fraction of the time must enhancement 3 be used to achieve an overall speedup of 10?


    Exercise 6 a sol

    Exercise 6 - a (sol)

    • By applying Amdahl’s Law to three enhancements we find

      Overall Speedup= 1 / [(1 – ∑ FEi) + ∑ (FEi/ SEi)]

      = 1 / [1 – (FE1 + FE2 + FE3) + ((FE1/SE1) + (FE2/SE2) + (FE3/SE3))]

    • By replacing every known variable by its value in the equation, we get:

      10 = 1 / [1 – (0.3 + 0.3 + FE3) + ((0.3/30) + (0.3/20) + (FE3/10))]

    • Solving for FE3 we get

      1 = 10 x (1 - 0.3 - 0.3 + 0.3/30 + 0.3/20 - FE3 + FE3/10) = 4.25 – 9FE3

    • Which means FE3 = 3.25 / 9 = 0.361111…

    • Thus, Enhancement 3 must be used around 36% of the time.


    Exercise 6 b

    Exercise 6 - b

    b. Assume for some benchmark, the fraction of use is 15% for each of enhancements 1 and 2 and 70% for enhancement 3. We want to maximize performance. If only one enhancement can be implemented, which should it be? If two enhancements can be implemented, which should be chosen?


    Exercise 6 b sol

    Exercise 6 – b (sol)

    • When we can choose between enhancements, we pick the one or combination that offers the highest speedup. Following that logic, and if we can pick only one enhancement,

      SpeedupE1= 1 / [(1 – FE1) + (FE1/SE1)] = 1 / [(1 – 0.15) + (0.15/30))] = 1.169

      SpeedupE2= 1 / [(1 – FE2) + (FE2/SE2)] = 1 / [(1 – 0.15) + (0.15/20))] = 1.166

      SpeedupE3= 1 / [(1 – FE3) + (FE3/SE3)] = 1 / [(1 – 0.70) + (0.70/10))] = 2.703

    • Since the Speedup provided by enhancement 3 is the highest, we choose it.


    Exercise 6 b sol1

    Exercise 6 – b (sol)

    • But if two enhancements can be implemented, we will need to find the best combination which means finding the speedup for all combinations and comparing them

      SpeedupE1 and E2 = 1 / [(1 – FE1 – FE2) + (FE1/SE1 + FE2/SE2)]

      = 1 / [(1 – 0.15 – 0.15) + (0.15/30 + 0.15/20))] = 1.403

      SpeedupE1 and E3 = 1 / [(1 – FE1 – FE3) + (FE1/SE1 + FE3/SE3)]

      = 1 / [(1 – 0.15 – 0.70) + (0.15/30 + 0.70/10))] = 4.444

      SpeedupE2 and E3 = 1 / [(1 – FE2 – FE3) + (FE2/SE2 + FE3/SE3)]

      = 1 / [(1 – 0.15 – 0.70) + (0.15/20 + 0.70/10))] = 4.396

    • Since the Speedup provided by the combination of enhancements 1 and 3 is the highest, we choose them.


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