Number System

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Number System

• Whats the most natural way to count?

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Number System

• Whats the most natural way to count?Use your
  hands. ( or maybe feet too! )

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Number System
In ancient times, people use notches Whats
the problem?
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Number System

• The need for a number system to count. -- a
  small set of symbols-- has to be convenient for
  calculation-- has to cover all the numbers, of
  course
• What are some of the number systems that we are
  using?

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Number System

• Decimal numbers
• Money!
• Roman numerals.
• Why decimals?

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Number System

• Roman NumeralsI (1), II ( 2 ), III ( 3)
  What is 4 ?

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Number System

• IV ( 4 )
• V ( 5 ), VI ( 6 ) IX( 9 ), X( 10 ), XI (
  11 ) L ( 50 ), C ( 100 ) , D ( 500 )

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Number System

• How good is it?

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Number System

• CDXLVIII is 448

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Number System

• 600 AD The Arabic number system is started. In
  15th Century, it is prevalent in Europe.So the
  Arabic decimal number system is great for us.
  But is it good for every body?

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Number System

• Whats a decimal system? Whats base-10?
• Really, 657 6 100 5 10 7 1
  6 102 5 101 7 100

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Number System

• So what base would E.T. use?

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Number System
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Number System

• 657 ( in E.T.s system) 6 82 5 81
  7 80 ? ( in decimal )

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Number System

• 657( Octal ) 431 ( in decimal )What about
  computer? Which base would it like to use?

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Number System

• 1011 1 23 0 22 1 21 1 20
• 11 ( in decimal )

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Number System

• To do addition in binary 1011
  1010 10101

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Number System

• What else can we do with numbers other than
  counting and arithmetic?

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Number System

• We can encode any symbols with numbers!!Hence,
  a computer can store all kinds of stuff by
  representing symbols as binary numbers.

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Number System

• Data!