CS150 - Fall 2013

CS150 - Fall 2013 - Class 24

administrative
   - final exam next week
      - what you can use:
         - final exam cheat sheet
            - Available on the course web page
            - I'll bring copies to the final
         - matlab basics handout (you bring it if you want it)
         - 2 pages of notes
      - besides that, closed book, closed notes, etc.
      - if you have special accommodations, e-mail me asap to let me know which exam you're taking and to figure out the details
   - final exam review on Friday

number representation
   - when you type:

      >> x = 17

      how does the computer actually store this information, specifically the number 17?

   - if you look far enough down into the details of what's going on when you run your computer, almost everything is represented using binary, i.e. some combination of 1's and 0's
   - why binary?
      - a combination of ease of use and cost
      - basic idea: "1" electrical current is flowing, "0" current is not flowing
      - transistors can do built to do this efficiently, cheaply and at a extremely small scale
      - could do other representations, but this is what is most effective right now... (and has been for a long time)

decimal numbers
   - most commonly used number systems have a "base"
      - each digit in the number can range from 0...base-1
      - each digit in the number has an index, starting at the right-most digit with 0 and working up to the left
      - the contribution of the digit is:

         base^index * value

      - by summing up the contribution of all of the digits, we get the value of the number

   - what is the base for our numbering system?
      - 10

      - for example
         - 245 = 5*10^0 + 4*10^1 + 2*10^2
         - 80498 = 8*10^0 + 9*10^1 + 4*10^2 + 0*10^3 + 8*10^4

binary numbers
   - we can represent numbers using any base we want
   - binary numbers are numbers represented as base 2
      - digits can only be a 0 or a 1

      - for example, the following binary numbers:
         - 101 = 1*2^0 + 0*2^2 + 1*2^2 = 5
         - 11 = 1*2^0 + 1*2^1 = 3
         - 10111 = 1*2^0 + 1*2^1 + 1*2^2 + 0*2^3 + 1*2^4 = 23
         - 100001 = 1*2^0 + 1*2^5 = 33

adding binary numbers
   - we can add binary numbers, just like we can add decimal numbers
   - to do it by hand, think back to how you did it in elementary school...
      - start at the right-most digits
      - add them together
      - if the sum < base
         - that's the value for that digit in the final sum
      - if the sum >= base
         - then carry a 1 over to the next column and subtract the base from the sum
         - the value for that digit is the sum - base
      - repeat for each digit
         - if there is a 1 carried over, also include that in the sum
   - binary addition works the same way:

   - we can check our answer
      - 10111 = 1 + 2 + 4 + 16 = 23
      - 101 = 1 + 4 = 5
      - 11100 = 4 + 8 + 16 = 28

subtracting in binary?
   - again, same idea as with decimal
      - work right to left
      - if the top digit > bottom digit
         - subtract the digits and store that as the answer
      - if the top digit < bottom digit
         - borrow 1 from the next number up (may have to keep looking up)
         - ...
      - ...

   - and again we can check our answer
      - 10001 = 1 + 16 = 17
      - 1010 = 2 + 8 = 10
      - 111 = 1 + 2 + 4 = 7

how do we represent negative numbers in binary?
   - remember, all we have is 1's and 0's (we can't do a negative sign '-')
   - one option...
      - indicate the sign with the most significant bit

         - 0101 = positive 101 = 5
         - 1101 = negative 101 = -5

      - any concerns with this approach?
         - two zeros (both a positive and a negative version)
            - 1000
            - 0000
         - turns out to be more work than other representations
            - have to check the sign bit when doing addition or subtraction
   - the way most computers do it: twos complement representation
      - http://en.wikipedia.org/wiki/Two's_complement

Course summarized
   - look at bbq.py code
   - look at url_basics.py code
      - we've come a long way!
      - you've learned how to program
   - 3 programming languages
      - Python
      - R
      - Matlab
   - Learned to interact with the file system through Terminal
   - 4952 lines of notes
      - assuming 34 lines per page: 145 pages of notes!
   - 1487 lines of code in the examples
      - ~110 different functions
   - you've written over 1200 lines of code yourself (and probably much more)
   - 2/3rds of the book
      - ~175 pages of reading
   - 21 problem sets