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Binary Mathematics. Counting system. There are three kinds of people in the world: those who can count, and those who can not. - Unknown Wisdom Today’s class Numbering system Conversion between 10 based and 2 based numbering system.

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Presentation Transcript

Counting system l.jpg
Counting system

  • There are three kinds of people in the world: those who can count, and those who can not.

    - Unknown Wisdom

  • Today’s class

    • Numbering system

    • Conversion between 10 based and 2 based numbering system.

    • Binary Mathematics.

    • Quiz


Base 10 counting system l.jpg
Base 10 counting system

  • We happened to use the current counting system, because we happened to have ten fingers.

  • If dinosaurs had ruled the earth, they would be happy to use a 8-based counting system.


Numbers l.jpg
Numbers

  • Ancient Africa

    • Notches on a bone.

  • Egyptians/Roman

    • Each magnitude is represented by a symbol.

  • Indian/Arabian (Modern numbering system)

1,475,268


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Base 10 (Decimal numbers)

  • What does 157 mean?

    • 157 = 1 x 100 + 5 x 10 + 7 x 1

      = 1 x 102 + 5 x 101 + 7 x 100


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Binary Code

  • Imagine a specie that only has two fingers. how can they count?

  • A computer is such kind of two-finger specie. 0 and 1

  • Each place is the exponential of 2


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Base 10 vs Base 2

Base 10

157

157 = 1 x 100 + 5 x 10 + 7 x 1

= 1 x 102 + 5 x 101 + 7 x 100

Base 2

1011 = 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20

1011 = 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1


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Binary Bits and Bytes

  • 1 bit is a single bit of information, a 1 or 0

    • Only two possible values

  • 1 byte is 8 bits, an 8 bit word

    • 256 possible values from 0-255 base 10 or 00000000 to 11111111 base 2

  • 10100110 is a single byte



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Binary mathematics

  • 0+0=0

  • 1+0=1

  • 1+1=10


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Hexadecimal (base 16)

  • Binary code is too long in representation. Hex is much shorter.

  • Converting a binary number to a Hex number is relatively easy

    • Every 4 bit can convert to a Hex

  • Problem: we are short of numbers

    • A-10 B-11 C-12 D-13 E-14 F-15




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Wisdom said

  • There are 10 kinds of people in the world, those who use binary counting system, and those who don’t.


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Quiz

  • No Calculators!!!!

  • Convert binary code to Decimal number.

    • 10100101 (Bin)

  • Convert Decimal number to binary code

    • 176 (Dec)

  • Convert Hexadecimal number to binary

    • BADDEF

  • Add these two binary numbers

    • 10001101+11011100=?


Answer l.jpg
Answer

  • 10100101 (Binary) = 165 (Decimal)

  • 176 (Decimal)= 10110000 (Binary)

  • BADDEF=1011,1010,1101,1101,1110,1111

  • The result of summation

    • 101101001


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