Chip Die size$($mm$2)$ Estimated defect rate$($per cm$2)$ Manufacturing size $($nm$)$ Transistors$($millions$)$

IBM Power $5389\mathrm{.}30130276$

Sun Niagara $380\mathrm{.}7590279$

AMD Opteron $199\mathrm{.}7590233$

Figure $1\mathrm{.}22$ Manufacturing cost factors for several modern processors.

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

you might make chips more cheaply if you placed an extra core on the die and

only threw out chips on which both processors had failed. We will solve this

exercise by viewing the yield as a probability of no defects occurring in a certain

area given the defect rate. Calculate probabilities based on each Opteron 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$.[20]<1\mathrm{.}6>$ What is the probability that a defect will occur on no more than

one of the two processor cores?

b$.[20]<1\mathrm{.}6>$ If the old chip cost $$20$ dollars per chip, what will the cost be of

the new chip, taking into account the new area and yield?