Due 5:00 PM, Wednesday Sept 25, on paper, in the box outside my office (Room 311, 3rd floor, CS building) or in class.
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Collaboration policy for COS 109:
Working together to really understand the material in problem sets and
labs is encouraged, but once you have things figured out, you must part
company and compose your written answers independently. That helps
you to be sure that you understand the material, and it obviates questions
of whether the collaboration was too close.
You must list any other class members with whom you collaborated. |
Problem set answers need not be long, merely clear enough that we can understand what you have done, though for computational problems, show enough of your work that we can see where your answer came from. There is no need to repeat the question, and it saves paper if you just give the answers. PLEASE submit typed material, not hand-written, and keep a copy for yourself just in case something goes astray. Thanks.
(a) Roughly how much would it cost to store a year's worth of metadata on generic 1 TB disk drives?
(b) Suppose instead that some mysterious US government agency with a 3-letter acronym wants to store the actual voice content of all the calls made in the USA in one year. Assume that a typical phone call is 3 minutes long and requires 1 MB to store. (It would be very easy to use less storage, so this is conservative.) About how many petabytes (PB) would be required to hold that information?
(c) Approximately what disk capacity would the NSA require to store 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.
(d) 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 you to drive a truck full of disks with the same information from California to New York?
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.
"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, 33, 63, 64, 65, 127, 128, 129, 255, 256, 257 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.
(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?
(c) (i) How many bits are needed to represent the current senior
class year (i.e., 2014) 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?
(d) (i) What range of numbers can you represent with the fingers and
thumbs of two hands if you treat each finger and thumb as a binary
digit?
(ii) Draw a picture of a pair of hands displaying the number 132.
(No artistic talent is required or expected.)
