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Number System

Discover the evolution of number systems from ancient notches to modern binary, explore the convenience of decimal and Roman numerals, and delve into the significance of different bases in arithmetic and computing.

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Number System

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  1. Number System • What’s the most natural way to count?

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

  3. Number System In ancient times, people use notches What’s the problem?

  4. 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?

  5. Number System • Decimal numbers • Money! • Roman numerals. Why decimals?

  6. Number System • Roman NumeralsI (1), II ( 2 ), III ( 3) What is 4 ?

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

  8. Number System • How good is it?

  9. Number System • CDXLVIII is 448

  10. 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?

  11. 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

  12. Number System • So what base would E.T. use?

  13. Number System

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

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

  16. Number System • 1011 = 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 =11 ( in decimal )

  17. Number System • To do addition in binary 1011 + 1010 10101

  18. Number System What else can we do with numbers other than counting and arithmetic?

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

  20. Number System • Data!

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