Answer the following questions. Show your calculations to get full points. 1. Yo
ID: 3727640 • Letter: A
Question
Answer the following questions. Show your calculations to get full points. 1. Your favorite program runs in 12 seconds on computer X, which has a 2.2 GHz clock. We are trying to help a computer designer build a computer, Y, which will run this program in 5 seconds. The designer has determined that a substantial increase in the clock rate is possible, but this increase will affect the rest of the CPU design, causing computer Y to require 1.5 times as many clock periods as computer X for this program. What clock speed should we tell the designer to target? (2 points) Suppose there are two implementations of the same instruction set architecture. Computer X has a clock cycle time of 125 ps and a CPI of 2.0, and computer Y has a clock cycle time of 200 ps and a CPI of 1.2 for the same program. Which computer is faster for this program and by how much? (2 points) For a certain microprocessor, consider that we have 25 unique instructions, 45% of those instructions require 3 clock cycles and the rest takes 2 clock periods. What is the average CPI? (1 point) 2. 3. 4. In a computer with the microprocessor of question 2 (having a CPI of 2.45), if I have a program to run, which has 323425 instructions, what is the clock rate I need in that processor to finish the program in 1 second? (2 point) According to the trend in device scaling observed by Moore's law, the number of transistors on a chip in 2018 should be how many times the number in 2000? (1 point) Assume you have a program that runs in 150 seconds on your computer. Out of that 150 seconds of the execution time, 75% is spend on multiplication operations. How much do you have to improve the speed of multiplication if you want the program to run 10 times faster? (2 points) 5. 6.Explanation / Answer
1. The program of x instructions takes 12 seconds on a CPU of 2.2GHz
A program of 1.5x instructions takes 5 seconds on a CPU of 12 * 1.5 * 2.2 / 5 GHz = 7.92GHz
(1.5x instructions would take 1.5 * 12 = 18 seconds on the 2.2GHz CPU. 18 * 2.2 = ? * 5 )
2. Time for one instruction in machine X = 2 * 125ps = 250ps
machine Y = 1.2 * 200ps = 240ps
Therefore, Y is 25/24 times faster than X.
3. Average CPI = ((45% of 25 * 3) + (55% of 25 * 2)) / 25 = 2.45
4. Clock rate = No. of instructions * CPI / time = 323425 * 2.45 = 792391.25 Hz
5. Moore's law states that the no. of transisters per square inch on a chip doubles every two years.
2018-2000=18
2^(18/2) = 512
6. In order to be ten times faster, the program must be completed in 15 seconds.
25% of 150 = 37.5 seconds
Therefore, regardless of how much faster the multiplication process is, the program will not complete in less than 37.5 seconds. The program cannot run 10 times faster by improving the speed of the multiplication process alone.
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