Day 12, MAT115

Last Time

Next Time

Announcements:
- Return of your prime/counting hw, and a couple of keys
- You have an assignment due today (to carry out some Egyptian multiplications and divisions). This is in preparation for your exam on Friday -- this very upcoming Friday! The exam will cover everything we've done up to (and including) Egyptian multiplication and division.
- Last time:
  - More Egyptian division, using the unit fraction table.
Today:
- I'd like to start by answering any questions you may have in preparation for the exam. Your exam will be primarily computational, but there will also be some questions from the various readings you've been assigned (some of the questions very simple, just to check if you actually read the material).
- Today's Topic: Busting up numbers (bases)
  - Queston of the day: How is Fraudini's trick related to base 2?
  - So far we've been busting up numbers in different ways. The first way was illustrated by the number 1729, and its base 10 representation.
    When we say "Seventeen twenty nine", what do we mean?
    What does each of the digits in the number 1729 mean?
    - The story of base 10....
    - Place value -- each power has its place
    - One of my favorite early introductions to bases was Tom Lehrer's New Math.
    - What's the story of base 2? Of base 8? Of base 20?
  - The Great Fraudini writes numbers in base 2 (see p. 11 of our text) -- that is, using powers of two.
    - 47=32+8+4+2+1
    - 89=64+16+8+1
    How would we write these numbers in base 2?
    - 47=101111
    - 89=1011001
    How can we understand this representation?
  - For your homework, you should have read this bases reference. Other bases are used constantly -- for example, in this web page. How so?
    - This page uses HTML to control its appearance. For example, the background color for this page is given by the command
      <body bgcolor="#FFF8DC">
      What does #FFF8DC have to do with color?
    - What are some other bases that we use in our lives? Where?
  - Translating between bases
    - Write 53 (written here in base 10) in base 2
    - Write 100101101 (written here in base 2) in base 10
    - Write 53 (written here in base 10) in base 8
    - Write 100101101 (written here in base 8) in base 10
    - Write 53 (written here in base 10) in base 16
    - Write 100101101 (written here in base 16) in base 10

Links:

Another unit fraction table, with other interesting links.
Horus

Website maintained by Andy Long. Comments appreciated.
Updated on 09/19/2011 14:20:33