Due 5:00 PM, Wednesday, Oct 21, 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) The integrated circuit chip that I designed around 1980 (passed around in class) used feature sizes of about 3.5 micrometers; today's chips have feature sizes of about 32 nanometers. If my original chip had about 10,000 transistors, very roughly how many would fit in the same area using today's feature sizes?
(b) If it takes one eon to play the Towers of Hanoi with 40 disks, about how many eons will it take to play with 60 disks? An expression is fine; there's no need to do arithmetic.
(c) During her visit to campus last October, Justice Ruth Bader Ginsburg described how before each session of the Supreme Court, each of the nine justices shakes hands with all the others. (i) What is the total number of handshakes? (ii) If there are N people doing handshakes, how does the total number of handshakes grow in proportion to N?
(d) An Apple Macbook Pro has a 15 inch screen (measured diagonally), while an Apple Cinema Display has a 30 inch screen. Assume that the pixels are the same size and the ratio of height to width is the same on both displays. (i) If the smaller display has 1.5 M pixels, how many pixels are there on the bigger display? (ii) If it uses the standard RGB representation of colors, how many MB of memory is required to hold the image of what's on the screen of the larger display?
(e) The lots of numbers video says that a new fiber optic cable transmits at 14 Tbps, equivalent to "2660 CDs or 210 million phone calls". (i) Is the number of CDs much too big, much too small, or about right? (ii) Assuming that 210 M is correct, what is the approximate rate in bits per second required by a single phone call? Explain your answers quantitatively.
(f) "We are living in exponential times," says the video, before noting that the number of text messages per day went from 1 in 1992 to 8 billion today. Assuming (quite improbably) that the number of messages doubled smoothly over this period, how many times did it double? Roughly how long does it take to double each time?
(a) The numbers video says that MySpace has 200 million users. If each user is given a unique identifying number, how many bytes are necessary to store the id of an individual user?
(b) "The surging popularity of the Twitter messaging service has
broken at least one Twitter client application and affected another as a
part of what is being called "the Twitpocalypse." Each message on
Twitter is assigned a unique identification number. On Friday evening,
the number of tweets exceeded 2,147,483,647." (Macworld.com, 6/13/09)
(i) Computers often store and process integers with one bit to
represent the sign (positive or negative) and the remaining bits to
represent the value. What is the likely size of the integers being used
by Twitter's computers, in bytes?
(ii) If the computer used a representation that assumed all numbers
were positive (no sign bit), what would be the number where the value
becomes too big? Use an expression; you don't need to compute it
exactly.
(c) We have discussed claims that the number of losses of personal data through theft, carelessness, bugs, etc., has reached at least 200 million. Assuming that each data item consists of a name, an address, and a social security number, which is the smallest of these devices with enough capacity to reasonably hold all of that lost data? Justify your answer quantitatively, stating any assumptions clearly.
1 GB iPod Shuffle 8 GB USB flash memory 100 GB hard disk 1 TB server disk
(d) How old is Cecilia, in decimal, binary and hexadecimal?