HW1Solution - Homework 1 Grading Key Prof Milos Prvulovic...

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Homework 1 Grading Key Prof. Milos Prvulovic CS 4290/6290 - Spring 2009 Handed Out: 15 Jan 2009 (Thu) Due: 29 Jan 2009 (Thu) This homework counts as 5% of the overall class grade. Submit your answers in T-Square as a single PDF document. You can either hand-write your answers and scan them into a PDF document, or write your answers in a text processor (e.g. LaTeX) and generate a PDF document from that (e.g. pdflatex). No printed submissions will be accepted. In case you hand-write your answers, keep in mind that illegible answers will be considered to be wrong answers. 1. Hennessy and Patterson textbook, Exercise 1.2 (pages 55-56). [25 points] a) [5 points] Using the first formula from page 22 of the book (dies per wafer) we get the number of dies per wafer of 147 (remember to round down, we can only use whole dies). [-0 points if number is around 180 (divide wafer area by chip area)] [-2 points if the number is below 140 or above 190] Using the second formula from page 22 of the book (die yield) with α =4 and wafer yield of 1 (no bad wafers) we get a yield of 0.36. Note: defect rate is given per cm^2, die area is given in mm^2, so remember to convert die area into cm^2 before you use the formula. [-2 points if using the wrong formula here] [-1 point if not using matching units for die area and defect rate] So we have 52.80 good dies per wafer, which makes the cost of a die $9.47. b) [5 points] For the new chip, we use the same approach but with a different die area and defects per cm^2. [Grading same as for part a] We get 107.23 good chips per wafer, at a cost of $4.66 per chip. c) [5 points] We were selling old chips for $13.26 each (1.4 times cost), profiting $3.79 per chip. [All or nothing, profit should be 40% of cost computed in part a] d) [5 points]
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We can sell a new chip for $26.52 (twice as much as before), profiting $21.86 per chip. [All or nothing, profit should be computed using numbers from parts c (old selling price) and b (cost of new chip)] e) [5 points] We made a profit of $1,895,000 per month [1 point] (500,000 times the per-chip profit) with old chips, and with new chips we will profit $32,790,000 per month [1 point] (1,500,000 times per-chip profit), so the increase in monthly profit is $30,895,000 [2 points]. The facility cost us $1,000,000,000, so we need 32.37 months [1 point] (almost 3 years) to recoup the cost of the new facility. [Note: Should use profits computed in parts c and d] [-2: for not considering difference of old profit and new profit to calculate the recoup time, i.e. students used: recoup time = investment/(new chip price x new chip sales)] [-2: considering old profit to calculate recoup time (students used: recoup time = investment/(old chip price x old chip sales). NOTE: all students who didn't consider new profit, they naturally didn't consider profit-difference, so they lost -4)] 2. Hennessy and Patterson textbook, Exercise 1.13 (page 62). [30 points] a) [5 points] The table does not give execution times, it gives “performance” relative to some (slow) reference machine, so we cannot compute weighted execution times easily.
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