1 / 18

Binary Mathematics

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.

lyris
Télécharger la présentation

Binary Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Binary Mathematics

  2. 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

  3. 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.

  4. Numbers • Ancient Africa • Notches on a bone. • Egyptians/Roman • Each magnitude is represented by a symbol. • Indian/Arabian (Modern numbering system) 1,475,268

  5. 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

  6. 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

  7. 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

  8. 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

  9. Base 10 to Binary

  10. Binary mathematics • 0+0=0 • 1+0=1 • 1+1=10

  11. 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

  12. Lookup table

  13. Example

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

  15. 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=?

  16. Answer • 10100101 (Binary) = 165 (Decimal) • 176 (Decimal)= 10110000 (Binary) • BADDEF=1011,1010,1101,1101,1110,1111 • The result of summation • 101101001

More Related