Do all of the following problems. Upload your responses here.

You must type your homework, whether in Word or another editor capable of handling all of the necessary notation – learning to do that in Word or in something else effective is part of the assignment. In Word, if you need more than standard text, try selecting the Insert tab and clicking on Equation near the right of the ribbon.

You must submit in PDF.

CPU Performance: Amdahl’s Law

Consider a CPU load that is, timewise:

• 20% integer instructions
• 10% branching instructions
• 70% floating point instructions.

Given that, what will be the speedup from:

1. Improving the overall integer performance of the ALU by a factor of 1.7?
2. Improving the overall floating point performance of the ALU by a factor of 1.2?
3. Improving the overall performance of branching logic by a factor of 4?

Consider a CPU with a standard five-stage pipeline. Assume that:

• Without stalls, all instructions take the same amount of time
• 10% of instructions are branches
• We have branch prediction that is successful 95% of the time
• When branch prediction fails, the penalty is a 3-cycle stall
• Current CPI is 2.1

Given all that:

1. What would CPI become if we improved branch prediction to a 98% success rate?
2. What would CPI become if we improved the failure penalty to a 1-cycle stall?

Memory Performance: Cache Equations

Consider a DRAM memory. Assume that:

• The memory has a single level of cache
• Checking the cache takes zero time
• Cache access time is 2ns
• DRAM access time is 30ns
• Accessing memory on a miss requires accessing the DRAM then accessing the cache to retrieve
• The current effective access time is 11ns

Given all that:

1. If the current effective access time is 11ns, what is the current hit rate?
2. What would the effective access time be if we subtracted a flat 5% from the hit rate?
3. What hit rate would we need for an effective access time of 3ns?

Storage Performance: Mixed Methods

Consider a spinning HDD with a random access time of 90ms and an effective transfer rate of 60MB/s. Now consider an SSD with a random access time of 100μs and an effective transfer rate of 500MB/s. Assume all files are contiguous and that seeks within otherwise contiguous reads take negligible time.

1. What will the speedup of the SSD over the HDD be when reading 5,000 files totaling 140MB? (Amdahl’s Law will not help you here, but you have enough information to determine the answer without it.)
2. What will the speedup of the SSD over the HDD be when reading 130 files totaling 1GB? (Amdahl’s Law will not help you here, but you have enough information to determine the answer without it.)

Assume the chance of a single hard drive failing in a given year is 7%. What are the chances, over that year, of:

1. Losing data from a 2-disc RAID 0 array?
2. Losing data from a 2-disc RAID 1 array?
3. Losing data from a 4-disc RAID 5 array? (Ignore the secondary URE problem.)