Number system
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Number System PowerPoint PPT Presentation


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Number System. What’s the most natural way to count?. Number System. What’s the most natural way to count? Use your hands. ( or maybe feet too! ). Number System. In ancient times, people use notches What’s the problem?. Number System.

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Number System

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Number system

Number System

  • What’s the most natural way to count?


Number system1

Number System

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


Number system

Number System

In ancient times, people use notches

What’s the problem?


Number system2

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?


Number system3

Number System

  • Decimal numbers

  • Money!

  • Roman numerals.

    Why decimals?


Number system4

Number System

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


Number system5

Number System

  • IV ( 4 )

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


Number system6

Number System

  • How good is it?


Number system7

Number System

  • CDXLVIII is 448


Number system8

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?


Number system9

Number System

  • What’s a decimal system? What’s base-10?

  • Really, 657 = 6 * 100 + 5 * 10 + 7 * 1 = 6 * 102 + 5 * 101 + 7 * 100


Number system10

Number System

  • So what base would E.T. use?


Number system11

Number System


Number system12

Number System

  • 657 ( in E.T.’s system) = 6 * 82 + 5 * 81 + 7 * 80 = ? ( in decimal )


Number system13

Number System

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


Number system14

Number System

  • 1011 = 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20

    =11 ( in decimal )


Number system15

Number System

  • To do addition in binary 1011 + 1010 10101


Number system16

Number System

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


Number system17

Number System

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


Number system18

Number System

  • Data!


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