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Number System - PowerPoint PPT Presentation

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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Presentation Transcript

• What’s the most natural way to count?

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

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!