Graded out of 32; median was 27. 1. Round and Round We Go (a) Approximately what disk capacity would be required to hold everything you have heard in your life so far, in MP3 format? To unify everyone's computations, assume that you are 20 years old, and that you're listening all the time even when you're asleep. Remember what we said about significant figures: if the inputs to a computation are approximate, the output is only an approximation as well. 20 * 365 * 24 * 60 minutes is about 10.5 M minutes so it's about 10 or 11 TB; i would also take 10.5 TB (or the equivalent in any correct units) but it doesn't warrant any more precision than this. (b) A news story on 3/8/09 about software piracy said that the Pirate Bay's servers contained about 65 terabytes of files, corresponding to around 16,000 full-length movies. If 16,000 is right, about many gigabytes are there in a typical movie? What independent information do you have that would tend to support or contradict this value? ("Use the notes, Luke.") 65 * 10^12 / 16 * 10^3 is about 4 * 10^9, or 4 GB the notes say somewhere that a DVD holds 4.7 GB (c) Companies like Google and Facebook have multiple data centers that store copies of their information. If a company builds a new data center, it must clone the data from an existing data center. Suppose that a data center has 10 PB of data. (i) How long would it take to send the information over a 100 Gbps data link? (ii) How long would it take to ship a bunch of disks from California to New York by truck? In both parts, ignore overhead and delays; this question is entirely about transfer rates. And pay attention to units: B is conventionally bytes and b is bits. 10 PB is 10^16 bytes 100 Gbps is about 10^10 bytes/second so 10^6 seconds so at least 10 days a truck ought to be able to drive say 2500-3000 miles in 4-6 days anything that gets these basic ideas right and does sensible arithmetic on them is worth full credit. it would be nice to slightly penalize people who blindly look things up on google instead of estimating for themselves. for example, google says it's 2912 miles from here to san francisco and will take "1 day, 23 hours". if someone were to quote the driving time as 47 hours, that's an example of too much precision (since i didn't say where in california) (d) If the platter in the disk in a classic iPod is 1 inch in diameter and rotates at 3,600 revolutions per minute, about how fast in inches per second is the surface of the platter traveling past the read head at the outermost edge of the disk? If a desktop disk platter is 3.5 inches in diameter and rotates at 7,200 rpm, how fast is the surface traveling at its outermost edge? 3600 rpm is 60 rps circumference is pi 60 * 3.14 = 188 so about 190 inches/sec? anything in this range, and i don't mind a couple of significant figures here. 7 times faster than the previous, since diameter is 3.5x and speed is 2x. it would be interesting to know how many people recognized that no real work is necessary. 2. Bits, Bytes and Binary "There are only 10 types of people in the world: those who can read binary and those who can't." (a) Now that you get the joke, write out the decimal numbers 15, 16, 17, 31, 32, 63, 127 and 129 in binary and hex. (To be sure that you understand what you're doing, do the conversions between decimal, binary and hex by hand, not by a program or a calculator.) 15 1111 F 16 10000 10 17 10001 11 31 11111 1F 32 100000 20 63 111111 3F 127 1111111 7F 129 10000001 81 (b) An electronic car door key and its car must share some unique identification number so that my key won't unlock your car and vice versa. (i) Estimate roughly how many bits would be needed to provide each car in the United States with a unique identification number. Briefly explain your reasoning. (ii) How many bytes would this number require? suppose there are 200 million cars that takes 28 bits (2^28 is 268M) or 4 bytes any sensible estimate for the number of cars, say 100M < N < 300M? it's 4 bytes for any of those (c) (i) How many bits are needed to represent the current senior class year (i.e., 2012) as a binary number? (ii) How many bytes are needed? (iii) For what year will this number of bits increase? (iv) How many bytes will then be needed? 11 bits for 2012 2 bytes 2048 needs 12 bits (has to be exact) still 2 bytes (d) (i) What range of numbers can you represent with the fingers of two hands if you treat each finger as a binary digit but don't use your thumbs? (ii) What is the range if you can use your thumbs as well? (iii) Draw a picture of a pair of hands displaying the number 132. Assume that one uses fingers and thumbs. (You can submit a photograph if you prefer.) 0 .. 255 0 .. 1023 these have to be exact. | | 00|00 00|00 no penalty for lack of artistic talent. From Peng: The total is 32. The criteria is: Problem 1: total 12 (a) 2 pts (b) 2 pts (c) 2 pts for the data transmission time 2 pts for analysis on truck (If students just uses Google, I gave 1 pt penalty.) (d) 2pts for 190 inches/sec or 60pi inches/sec 2 pts for 3.5in disc Problem 2: total 20 (a) 4 pts (b) 3 pts for #bits 1 pt for #byte (c) 1 pt for 11 bits 1 pt for 2 bytes 2 pts for 2048 1 pt for 2 bytes (d) 2 pts for 0-255 (If students gave just 256 or 1024, not range, I gave 1 pt penalty) 2 pts for 0-1023 2 pts for 132 1 extra point is a gift.