1.3 [20/20/10/10/20] <1.7> Your colleague at Sun suggests that, since the yield is so poor, it might make sense to sell two sets of chips, one with 8 working processors and one with 6 working processors. We will solve this exercise by viewing the yield as a probability of no defects occurring in a certain area given the defect rate. For the Niagara, calculate probabilities based on each Niagara core separately
(this may not be entirely accurate, since the yield equation is based on empirical evidence rather than a mathematical calculation relating the probabilities of finding errors in different portions of the chip).
a. [20] <1.7> Using the yield equation for the defect rate above, what is the probability that a defect will occur on a single Niagara core (assuming the chip is divided evenly between the cores) in an 8-core chip?
b. [20] <1.7> What is the probability that a defect will occur on one or two cores (but not more than that)?
c. [10] <1.7> What is the probability that a defect will occur on none of the cores?
d. [10] <1.7> Given your answers to parts (b) and (c), what is the number of 6-core chips you will sell for every 8-core chip?
e. [20] <1.7> If you sell your 8-core chips for $150 each, the 6-core chips for $100 each, the cost per die sold is $80, your research and development budget was $200 million, and testing itself costs $1.50 per chip, how many processors would you need to sell in order to recoup costs?

1.2 [20/20/20/20/20] <1.7> You are trying to figure out whether to build a new fabrication facility for your IBM Power5 chips. It costs $1 billion to build a new fabrication facility. The benefit of the new fabrication is that you predict that you will be able to sell 3 times as many chips at 2 times the price of the old chips. The new chip will have an area of 186 mm2, with a defect rate of .7 defects per cm2.
Assume the wafer has a diameter of 300 mm. Assume it costs $500 to fabricate a wafer in either technology. You were previously selling the chips for 40% more than their cost.
a. [20] <1.5> What is the cost of the old Power5 chip?
b. [20] <1.5> What is the cost of the new Power5 chip?
c. [20] <1.5> What was the profit on each old Power5 chip?
d. [20] <1.5> What is the profit on each new Power5 chip?
e. [20] <1.5> If you sold 500,000 old Power5 chips per month, how long will it take to recoup the costs of the new fabrication facility?

1.6 [10/10/Discussion] <1.2, 1.9> Figure 1.24 gives a comparison of power and performance for several benchmarks comparing two servers: Sun Fire T2000 (which uses Niagara) and IBM x346 (using Intel Xeon processors).
a. [10] <1.9> Calculate the performance/power ratio for each processor on each benchmark.
b. [10] <1.9> If power is your main concern, which would you choose?

c. [Discussion] <1.2> For the database benchmarks, the cheaper the system, the lower cost per database operation the system is. This is counter intuitive:
larger systems have more throughput, so one might think that buying a larger system would be a larger absolute cost, but lower per operation cost. Since this is true, why do any larger server farms buy expensive servers? (Hint:Look at exercise 1.4 for some reasons.)