CS54 - Fall 2022 - Class 7

Lecture notes

  • admin
       - assignment 3 due Sunday
       - get started ASAP
       - If you work with a partner, only once person needs to submit on Gradescope

  • midterm
       - logistics
          - in class on Wednesday
          - pencil and paper exam (practice writing a few functions in SML on paper)
          - closed books, notes, computer, etc.
          - *except*, can bring two pages of notes (e.g., a double-sided piece of paper)

       - Coverage: SML
          - evaluate the function/what does the function do
          - type signature
          - code up functions
       - Extra mentors on Monday and Tuesday for review support
       - I will post *some* samples problems
          - Intro SML reading and books also have others

  • recursion patterns

  • difference between [] and [[]]

  • 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

  • other bases
       - we can represent values by any base we'd like!
       - A common one is CS, base 2, binary numbers:
          - 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
       - we can use any base we'd like, though
          - base 9
             - digits are numbers from 0 through 8
             - 267 = 7*9^0 + 6*9^1 + 2*9^2 = 7 + 54 + 162 = 223
          - base 200
             - digits are numbers from 0 through 199
             - 267 = 7*200^0 + 6*200^1 + 2*200^2 = 81,207
                - note that even numbers written the same way can be interpreted differently!
             - 2 55 167 = 167*200^0 + 55*200^2 + 2*200^2 = 91,167
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