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

4. 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 Numerals I (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 * 10 2 + 5 * 10 1 + 7 * 10 0

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

13. Number System

14. 657 ( in E.T.’s system) = 6 * 8 2 + 5 * 8 1 + 7 * 8 0 = ? ( 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 * 2 3 + 0 * 2 2 + 1 * 2 1 + 1 * 2 0 =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!