Ive got problems with big hairy gorillas on them.

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Ive got problems with big hairy gorillas on
them.
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• Gedde Watanabe in Gung Ho (1986)

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Computer Science 101Lecture 7
www.pjrc.com/tech/ 8051/board5/schematic.gif

• Spring Semester 2008
• Friday, January 25
• Week 3/18
• Albert H. Carlson

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Announcements

• HW 1 is due today, January 25
• HW 2 is due on Friday, February 8

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What Do We Do for Fractions?

• Normally, we show where the whole number ends
  and the fraction begins
• This is normally shown by a .
• 785.25
• What do we call this dot?
• We call it the radix point
• Everything to the right of the point is fractional

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• Since the number to the left of the radix is 100,
  then it only makes sense that the number to the
  right is 10-1
• 10-1 1/10 1/101 .1
• And, it just keeps going using the same logic

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So, What Bases Are There

• As many as you can imagine
• Only a few have proven useful over time. They
  include
• Base 2 (Binary)
• Base 8 (Octal)
• Base 10 (Decimal)
• Base 12 (No name, but based on dozens)
• Base 16 (Hexadecimal)

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What Can We Say About Them

• For a base n, there are n symbols 0 up to n-1
• Note, for base 3, for instance, there can be NO 3
  in the number
• Hexadecimal, or hex, has a problem we have no
  symbols for 10 through 16. We use a, b, c, d, e,
  f
• Denote bases by a subscript of the base after the
  number - 3458

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• Some bases are special and have different
  notation
• NO base indication for base 10 it is the
  default
• Use an H to denote hexadecimal 2a5H

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Numbers are a Language

• Numbers are a language just like combinations
  of letters
• The symbols are numbers the numbers are the set
  of symbols
• Lets say we have a cow. We will look at how
  different people say cow

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• Cow (English)
• ?????? (Russian word)
• ??? (Russian has the same rough sound)
• Note that in both languages we are saying the
  same thing
• The second one is just the same sound in a
  different language.

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• In effect, we are saying the same thing, but in
  order to understand it, we have to translate it
  into what we know
• Base conversion does that translation
• No matter what language we say it in, it means
  the same thing

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How Do We Do Math?

• The simple answer is Generally the same way
• Lets use base 2 for example
• In base two we have 2 numbers
• 0
• 1
• We are going to do the four basic math operations

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• Addition
• Subtraction
• Multiplication
• Division
• Lets start with addition
• Basic Facts
• 0 0 0
• 0 1 1 0 1
• 1 1 102
• 1 1 1 112

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Back to the Math

• It is not really different than what you are used
  to
• Lets do a simple example
• 111102 000112
• So, how do we start?
• We start by getting the problem set up like we
  normally do with addition

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1
1
1
1
11110 00011
1
0
0
0
0
1
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Practice Problems
101010 110011 1011101
111011 000101 1000000
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Subtraction

• Rules are simple
• 0 0 0
• 1 1 0
• 1 0 1
• 0 1 1, borrow the 1, or 102 1 1, borrow
  the 1
• The key is the borrow

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Doing the Subtraction

• An Example
• 11110
• -00001

1
0
\
1
0
1
1
1
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• Another Example
• 10000
• -00010
• 01110
• 101010
• -010101
• 010101

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Multiplication

• Again, multiplication looks a lot like decimal
  multiplication
• Here the terms are a lot easier
• 1 0 0 1 0 0 0
• 1 1 1
• The steps are the same
• Multiply by the number in question
• Write down the answer
• Shift left, and repeat until done

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• An example
• 1010
• x0101

1010
0000
1010
0000
0110010
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Practice Problems

• 1111
• x1000
• 1111000
• 0110
• x1001
• 110110

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Questions?