REDIRECTING
Please  wait  FisadDi  is  on  the  way.

FisadDi

FisadDi.com
4. Positional Numbering System Part 4 (Conversion Octal to Decimal, Binary & Hexadecimal)

Download Notes

Computer Organization & Architecture

1. Positional Numbering System (Conversion from Octal to Decimal, Binary and Hexadecimal)


  1. Conversion from Octal to Decimal:-

◼ Isme hum convert krenge base 8 ko base 10 main ()8 = ()10.
◼ Jaise humne Binary se Decimal me conversion kiya tha rough work main table ko use krk waise hi table isme use krnge bs iska base 8 hoga kuki hum octal se conversion kr rhe hai.
◼ (1101011)2 = (?)10
    Toh main avi table batane ja rha hu octal base 8 k liye jaise humne binary me table ko use kiya tha waise hi use krnge lekin kevel rough work k liye.
◼ Table betane se phele main two point btaunga jisse krne se octal to decimal nikal saktey hai:-
  ◼ Phela point yeh hai ki agar 82 = 8 * 8 = 64 hota hai jo hum 8 ki 8 me ek bar multiply kar ke dekh sakte h.
  ◼ Agar 83 = 8 * 8 * 8 =512 hota hai 8 ko 3 bar multiply karke.
  ◼ Agar 84 = 8 * 8 * 8 * 8 =4096 hota hai 8 ko 4 bar multiply karke.
  ◼ Isko krne se answer to nikl jayega lekin time lagega or pareshani bhi hogi .
◼ To ek easy trick h.
  FisadDi_Image
◼ Dusra point yeh hai ki joh maine table benaya hai isse hum easy answer nikal sektey hai.
  ◼ Jaise maine binary ka table betaya tha usko use krk solve kr sektey hai.
  ◼ Hume 1 se start karke double karte jana h 1, 2, 4, 8, 16, 32, 64 _ _ _ infinite.
  ◼ Or ye easy h fir agar mujhe 83 chahiye to m 8 par jo power h yani 3 ko 3 se multiply kar dunga 3 * 3 = 9.
  ◼ To hum 10 bar double kate jayenge 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 to 3 * 3 = 29 = 83 = 512.
  ◼ Aise hi agar mujhe 84 chahiye to m 4 ko 3 se multiply kar dunga 4 * 3 = 12 kyoki power m 4 h.
  ◼ To is bar hum 13 bar double karte jayenge jab hamara pehle answer aya 9 to humne 10 bar double kiya or jab hamara answer aya 12 to hum 13 bar karenge matlab answer m 1 ko add kar denge 12 + 1 = 13 kyoki hum 1 se start karte h or 20 ki value hoti h 1 power 0 se start hoti h hamesha.
  ◼ 0 , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ye sab 2 ke uper power h.
  ◼ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096 to 4 * 3 = 212 = 84 = 8192.
  ◼ Ye sabhi aapko aapki ungali par kar loge bohot easy h.
  ◼ 81 = 8 hota hai kyoki 1 * 3 = 3 .
  ◼ 23 = 8
  ◼ 82 = 64 hota hai kyoki 2 * 3 = 6 .
  ◼ 26 = 64
  ◼ 83 = 512 hota hai kyoki 3 * 3 = 9 .
  ◼ 29 = 512
  ◼ 84 = 4096 hota hai kyoki 4 * 3 = 12 .
  ◼ 212 = 4096
  ◼ 85 = 32768 hota hai kyoki 5 * 3 = 15
     simply 4096 * 2 * 2 * 2.
  ◼ 215 = 32768
  ◼ Hum dakh rhe hai ki easily calculation ho rha hai agar aise use kr rhe hai toh.
◼ Let's take an example
    (5126)8 = (?)10
  FisadDi_Image
◼ Sabse phele toh aise likh lenge jaise image me diya hua hai.
  FisadDi_Image
◼ Uske baad joh yha binary ko multiply kiya hai usko kaise kiya yeh dekhiye .
◼ 83 = 29, 82 = 26, or 81 = 23
◼ Kaise hua yeh main beta chukka hu Phir usk bad multiply or addition krne k baad Joh result aya woh likh denge.
       (5126)8 = (2646)10
  2. Conversion from Octal to Binary:-
◼ Isme hum convert kernge base 8 ko base 2 main ()8 = ()2
◼ Let's take an example
    (453)8 = (?)2
  FisadDi_Image
◼ Is image main hum kya kr rhe hai ki, sabse phele number ( 453) ko alag alag likh lenge fir sabhi alag number ka binary m convert kar lenge.
◼ Convert karne ke liye    4    2    1    ko use karenge or jo limit ke m hoga uske niche 1 or jo limit se bahar h uske niche 0 likh denge.
◼ Jaise 3 ke liye 4 3 se bada h to 4 ke niche 0 2 or 1 ke niche 1 kyoki dono ko add karne par 3 ke barabar h to 3 ka binary 011 hua.
◼ fir sabhi alag binary ko jode denge lekin usi sequence m jis m octal number lkha tha matlab ki sabse pehle 4 ka binary fir 5 ka binary or last m 3 ka.
  FisadDi_Image
◼ Divide kerne k baad jha se start from this side likha hai wha se start krk result jaise likha waise likh denge.
◼ Finally humara result aagya
       (453)8 = (100101011)2
  3. Conversion from Octal to Hexadecimal:-
◼ Isme hum convert krety hai base 8 ko base 16 main ()8 = ()16
◼ Isme hum kya krenge sabse phele Octal ko convert krna hoga Binary main phir Binary main jb convert kr lenge to usko hume Hexadecimal main convert krenge.
  FisadDi_Image
◼ Let's take an example
    (453)8 = (?)16
◼ Ye same waise hi hoga jaise abhi uper kiya Octal se Binary.
  FisadDi_Image
◼ Binary main convert krne k baad hume jo binary number mila usko hexadecimal main convert krne k liye 4-4 bit main divide kr denge jaise image main kiya hai lekin hum dekh rhe hai ki left most bit main 4 bit ni hai toh usko hum 4 bit me benane ke liye 1 ke pehle 3 0's add kar denge.
  FisadDi_Image
◼ Ab sbhi ko 4-4 bits main divide kar liya h.
  FisadDi_Image
◼ Hexadecimal main convert krne k liye table ka 8 4 2 1 lenge phir jha se start from here likha hai wha se likhenge jaise image main likha hai.
  FisadDi_Image
◼ Jaise hexadecimal main convert ho gya hai jaise image main kiya hai usk baad result likh denge jaise image main likha hai.
◼ Finally humara result aa gaya.
       (453)8 = (12B)16

<-------------------END------------------>

Agar aapko iss Topic m kuch bhi problem h to aap husme freely puche
Fisaddi.helpdesk@gmail.com

Thank You
Team FisadDi

Download Notes


About Us

Hello Friends, FisadDi is working to help students with their subjects. We provide videos as well as text notes in hindi language to make study easy. Our agenda is not only to help students to get good marks but also they will get the right knowledge and learn how the things work in a very easy way in their mother tongue. We are working hard to help in making your bright future.


Thank You
Team FisadDi


Contact Us

contact.fisaddi@gmail.com

Ghaziabad, India

8376873936


 
   
 
© www.fisaddi.com. All Rights Reserved.