CSCI 370 Computer Architecture: Homework 1

Due date: On or before Monday, February 12, 2024 Absolutely no copying others’ works

Name: ___________________________

• Upload the completed homework to the section of “COVID-19 Exams, Homeworks, & Programming Exercises” of Blackboard.
• The purpose of homeworks is for students to practice for the exams without others’ help, so the penalty of mistakes will be minor.
• Without practicing for the exams properly, students will not be able to do well on the exams.

---

1. Consider two different processors P1 and P2 executing the same instruction set with the clock rates and CPIs given in the following table:
   
   

   Processor	Clock Rate	CPI
   P1	2.5 GHz	2.0
   P2	2.0 GHz	1.5

   
   
   1. (15%) Which processor has the higher performance expressed in instructions per second?
      Ans>
      
      • Instructions/second_P1 =
      
      
      
      
      • Instructions/second_P2 =
      
      
      
      
      The higher performance:
   
   
   
   2. (20%) If the processors each execute a program in 15 seconds, find the number of cycles and the number of instructions.
      Ans>
      
      • # of instructions_P1 =
      
      
      
      
      • # of instructions_P2 =
      
      
      
      
      • # of clock cycles_P1 =
      
      
      
      
      • # of clock cycles_P2 =
      
      
      
      
   
   
   
   3. (20%) We are trying to reduce the execution time (15 seconds) by 15% but this leads to an increase of 10% in the CPI. What clock rate should we have to get this time reduction?
      Ans>
      
      • Clock rate_P1 =
      
      
      
      
      
      • Clock rate_P2 =
      
      
      
      
   
   
   
2. Compilers can have a profound impact on the performance of an application. Consider the following two compilers for a program:
   
   

   Compiler A		Compiler B
   Instruction count	Execution time	Instruction count	Execution time
   2.0×109	2.0 s	1.0×109	2.5 s

   
   
   1. (15%) Find the average CPI for each program given that the processor has a clock cycle time of 2 ns (or 2×10^-9 s).
      Ans>
      
      • Average CPI_A =
      
      
      
      
      
      • Average CPI_B =
      
      
      
      
   
   
   
   
   2. (15%) Assume the compiled programs 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’s code versus the clock of the processor running compiler B’s code?
      Ans>
      
         Clock rate_A / Clock rate_B (or Clock cycle time_B / Clock cycle time_A)
      =
   
   
   
   
   
   
   
   3. (15%) A new compiler is developed that uses 4.5×10⁸ instructions and has an average CPI of 3.0. What is the speedup of using this new compiler versus using Compiler A on the original processor?
      ^†Hint: The speedup here is equal to TA/Tn where
      • TA: the execution time by using the A compiler and
      • Tn: the execution time by using the new compiler.
      Ans>
      
         TA/Tn
      =