Complete the following problems and show ALL work!  Each problem is worth 10 points.

1. Show how the following values would be stored by byte-addressable machines with 32-bit words, using little endian and then big endian format. Assume each value starts at address 1016. Draw a diagram of memory for each, placing the appropriate values in the correct (and labeled) memory locations.
a. 456789A116
b. 0000058A16
c. 1414888816

2. Convert the following expressions from infix to reverse Polish (postfix) notation.
a. X * Y + W * Z + V * U
b. W * X + W * (U * V + Z)
c. (W * (X + Y * (U * V)))/(U * (X + Y))

3. Write the following expression in postfix (Reverse Polish) notation. Remember the rules of precedence for arithmetic operators!

X = (A-B+C*(D*E-F))/(G+H*K)

4. Convert the following expressions from reverse Polish notation to infix notation.
a. W X Y Z – + *
b. U V W X Y Z + * + * +
c. X Y Z + V W – * Z + +

5. A nonpipelined system takes 200ns to process a task. The same task can be processed in a 5-segment pipeline with a clock cycle of 40ns. Determine the speedup ratio of the pipeline for 200 tasks. What is the maximum speedup that could be achieved with the pipeline unit over the nonpipelined unit?

6. A nonpipelined system takes 100ns to process a task. The same task can be processed in a 5-segment pipeline with a clock cycle of 20ns. Determine the speedup ratio of the pipeline for 100 tasks. What is the theoretical speedup that could be achieved with the pipeline system over a nonpipelined system?

For this homework you will be using a cache simulator called Camera which you can download at This site also contains instructions for how to use Camera.  If you do not have a Java compiler, get the compiled classes here.  To run the software, use the command line to move to the directory where the Camera files are and type java Camera.

Camera has four features:

7. Direct Mapped Cache Simulation

8. Set Associative Cache Simulation

9. Fully Associative Cache Simulation

10. Virtual Memory and Paging Simulation

Your goal here is to use the simulators to understand these different types of memory caches. To do this, you need to run each type of simulator and document/explain what it is doing. For the three the cache simulators, you need to compare and contrast them and analyze which scheme seems to be the best. For the Memory and Paging Sim, you need to run through the tutorial and document/explain what is it doing. Provide screenshots if you need to be as thorough as possible. Also, this should be written in your own words, not quoting from any material. As part of your write up, put together a line graph or bar chart that compares the number of cache hits and caches misses for each cache simulation.


11. Your friend has just bought a new personal computer. She tells you that her new system  runs at 1GHz, which makes it over three times faster than her old 300 MHz system. What would you tell her? (Hint: Consider how Amdahl’s Law applies.)

12. Suppose the daytime processing load consists of 60% CPU activity and 40% disk activity. Your customers are complaining that the system is slow. After doing some research, you have learned that you can upgrade your disks for $8,000 to make them 2.5 times as fast as they are currently. You have also learned that you can upgrade your CPU to make it 1.4 as fast for $5,000.
a. Which would you choose to yield the best performance improvement for the least amount of money?
b. Which option would you choose if you don’t care about the money, but want a faster system?
c. What is the break-even point for the upgrades? That is, what price would we need to charge for the CPU (or the disk – change only one) so the result was the same cost per 1% increase for both?

13. Suppose a disk drive has the following characteristics:
• 5 surfaces
• 1024 tracks per surface
• 256 sectors per track
• 512 bytes/sector
• Track-to-track seek time of 8 milliseconds
• Rotational speed of 7500 RPM.
a. What is the capacity of the drive?
b. What is the access time?

14. Suppose you have a 100GB database housed on a disk array that supports a transfer rate of 60MBps and a tape drive that supports 200GB cartridges with a transfer rate of 80MB per second. How long will it take to back up the database? What is the transfer time if 2:1 compression is possible?

15. A particular high-performance computer system has been functioning as an e-business server on the Web. This system supports $10,000 per hour in gross business volume. It has been estimated that the net profit per hour is $1,200. In other words, if the system goes down, the company will lose $1,200 every hour until repairs are made. Furthermore, any data on the damaged disk would be lost. Some of this data could be retrieved from the previous night’s backups, but the rest would be gone forever. Conceivably, a poorly-timed disk crash could cost your company hundreds of thousands of dollars in immediate revenue loss, and untold thousands in permanent business loss. The fact that this system is not using any type of RAID is disturbing to you. Although your chief concern is data integrity and system availability, others in your group are obsessed with system performance. They feel that more revenue would be lost in the long run if the system slows down after RAID is installed. They have stated specifically that a system with RAID performing at half the speed of the current system would result in gross revenue dollars per hour declining to $5,000 per hour. In total, 80% of the system e-business activity involves a database transaction. The database transactions consist of 60% reads and 40% writes. On average, disk access timeis 20ms. The disks on this system are nearly full and are nearing the end of their expected life, so new ones must be ordered soon. You feel that this is a good time to try to install RAID, even though you’ll need to buy extra disks. The disks that are suitable for your system cost $2000 for each 10 gigabyte spindle. The average access time of these new disks is 15ms with a MTTF of 20,000 hours and a MTTR of 4 hours. You have projected that you will need 60 gigabytes of storage to accommodate the existing data as well as the expected data growth over the next 5 years. (All of the disks will be replaced.)
a. Are the people who are against adding RAID to the system correct in their assertion that 50% slower disks will result in revenues declining to $5,000 per hour? Justify your answer.
b. What would be the average disk access time on your system if you decide to use RAID-1?
c. What would be the average disk access time on your system using a RAID-5 array with two sets of 4 disks if 25% of the database transactions must wait behind one transaction for the disk to become free?
d. Which configuration has a better cost-justification, RAID-1 or RAID-5? Explain your answer.

Which of the types of storage architectures discussed in this section would you expect to find in a large data center or server farm? What would be the problem with using one of the other architectures in the data center environment?

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