Due 5:00 PM, Wednesday, Oct 7, in the box outside Room 311, CS
building, or in class. Answers need not be long, merely clear so we can
understand what you have done. Please submit typed material, not
hand-written, if at all possible, and keep a copy for yourself just in
case something goes astray. Thanks.
(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.
(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.")
(c) Google has multiple data centers that store copies of their searchable information. If they build a new data center, they have to clone the data from an existing data center. Suppose that a center has 10 PB of disk space (I'm making this number up). Is it faster to ship a bunch of disks say from California to New York by truck or to send the information over a 100 Gbps data link? Explain your answer quantitatively. Ignore overhead and delays; this question is entirely about transfer rates. And pay attention to units: B is conventionally bytes and b is bits.
(d) If 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 information traveling past the read head at the outermost edge of the disk? If a desktop disk is 3.5 inches in diameter and rotates at 7,200 rpm, how fast is the information traveling at its outermost edge?
(e) An article in the New York Times on 2/7/09 said that the organization that manages the Harvard endowment grew by 33% under its previous manager, but the new manager is going to cut employment by 25%. If Harvard started with 75 employees in this group before the previous manager started hiring, how many will be left after the new manager finishes firing?
(f) Another article in the New York Times about the same time said that the ball used in a Chicago version of softball has a 16 inch diameter. What would be the circumference of this ball? A correction a couple of days later said that the circumference is 16"; in that case, what's the diameter of a Chicago softball? A regulation softball is 12 inches in circumference. What is the ratio of its diameter to a Chicago softball?
"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 jokes, write out the decimal numbers 15, 16, 17, 31, 32, 47, 63, 64, 99, 100 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) How many bits are needed to represent the current senior class year (i.e., 2010) as a binary number? How many bytes are needed? For what year will this number of bits increase? How many bytes will then be needed?
(c) "The human genome consists of some 2.9 billion of the letters AGCT, the equivalent of about 750 megabytes of data." (NY Times, 6/26/07) (i) If the letters are represented in ASCII, about how many megabytes would be required to store the representation of the genome? (ii) Give a binary representation of the letters AGCT that would make it possible to fit the genome into 750 MB.
(d) 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? What is the range if you can use your thumbs as well?
(e) Draw a picture of a pair of hands displaying the number 132. Assume that one uses fingers and thumbs.
