Your colleague at AMD suggests that, since the yield is so poor,

you might make chips more cheaply if you released multiple versions of the same chip, just with different numbers of cores. For example, you could sell Phoenix⁸,

Phoenix⁴, Phoenix², and Phoenix¹, which contain 8, 4, 2, and 1 cores on each chip,

respectively. If all eight cores are defect-free, then it is sold as Phoenix⁸. Chips with four to seven defect-free cores are sold as Phoenix⁴, and those with two or three defect-free cores are sold as Phoenix². For simplification, calculate the yield for a single core as the yield for a chip that is 1/8 the area of the original Phoenix chip.

Then view that yield as an independent probability of a single core being defect free. Calculate the yield for each configuration as the probability of at the corresponding number of cores being defect free.

a. What is the yield for a single core being defect free as well as the yield for Phoenix4, Phoenix2 and Phoenix1?

b. Using your results from part a, determine which chips you think it would be worthwhile to package and sell, and why.

c. If it previously cost $20 dollars per chip to produce Phoenix⁸, what will be the cost of the new Phoenix chips, assuming that there are no additional costs associated with rescuing them from the trash?

d. You currently make a profit of $30 for each defect-free Phoenix⁸, and you will sell each Phoenix⁴ chip for $25. How much is your profit per Phoenix⁸
chip if you consider

(i) the purchase price of Phoenix⁴ chips to be entirely profit and (ii) apply the profit of Phoenix4 chips to each Phoenix⁸ chip in proportion to how many are produced? Use the yields calculated from part Problem 1.3a, not from problem 1.1a.

■ Amdahl’s Law ■ Redundancy ■ MTTF ■ Power Consumption Power consumption in modern systems is dependent on a variety of factors, including the chip clock frequency, efficiency, and voltage. The following exercises explore the impact on power and energy that different design decisions and use scenarios have.