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Number System

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- What’s the most natural way to count?

- 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?

- 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?

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

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

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

- How good is it?

- CDXLVIII is 448

- 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?

- What’s a decimal system? What’s base-10?
- Really, 657 = 6 * 100 + 5 * 10 + 7 * 1 = 6 * 102 + 5 * 101 + 7 * 100

- So what base would E.T. use?

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

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

- 1011 = 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20
=11 ( in decimal )

- To do addition in binary 1011 + 1010 10101

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

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

- Data!