REDIRECTING
Please  wait  FisadDi  is  on  the  way.

FisadDi

FisadDi.com
1. Positional Numbering System Part 1 (Conversion Decimal to Binary)

Download Notes

Computer Organization & Architecture

1. Positional Numbering System(Conversion Decimal to Binary) :

There are four types of Positional Numbering System :
1. Decimal Number
2. Binary Number
3. Octal Number
4. Hexadecimal Number

I. Decimal Number :-
◼ Decimal Number ka base hota hai 10(Base 10).
◼ It is denoted by ( )10.
◼ Joh decimal numbers hota h uska base 10 kyu hota main ?
◼ Decimal number start hota hai 0 se or end hota hai 9 par (0,1,2,3,4,5,6,7,8,9).
◼ Toh kitna number hai total 10 number h isliye iska base 10 hota hai.
◼ Example:- (8971)10 iska base 10 or 8971 number 0 se 9 tak k number ka combination hai.
Note:- jb kisi bhi number ka base 10 ho toh decimal numbers hi hota h.

II. Binary Number :-
◼ Binary number ka base 2 hota hai(Base 2).
◼ It is denoted by ( )2.
◼ Joh Binary number hota hai uska base 2 kyu hota hai?
◼ Binary Number kevel 0 or 1 ka combination hota hai jaise(11010011) or (0010101) etc.
◼ Toh ye kitna number hua 2 (0 or 1) isliye isko Binary Number boltey hai.
◼ Example : ( 1000101)2 iska base 2 or (0,1) ka combination hai.
Note:- Jb kisi bhi number ka base 2 ho toh Binary Number hi hota hai.

III. Octal Number :-
◼ Octal Number ka base 8 hota hai(Base 8).
◼ It is denoted by ( )8.
◼ Joh octal number hota hai uska base 8 kyu hota hai?
◼ Octal Number start hota hai 0 se or end hota h 7 par(0,1,2,3,4,5,6,7).
◼ Toh kitna numbers hai total 8 numbers h isliye iska base 8 hota hai.
◼ Example : (17641)8 iska base 8 hai or 17641 number (0- 7) tak numbers ka combination hai.
◼ Octal m 8 or 9 nahi hoga jaise 8971 ye number octal nahi h kyo ki isme 8 bhi h or 9 bhi.
Note:- jab kisi bhi number ka base 8 ho toh usko Octal Number boltey hai.

IV. Hexadecimal Number :-
◼ Hexadecimal Number ka base 16 hota hai(base 16).
◼ It is denoted by ( )16.
◼ Joh Hexadecimal Number hota hai iska base 16 kyu hota hai?
◼ Hexadecimal number start hota hai 0 se or end hota hai 15 par(0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15).
◼ Toh yha par total 16 numbers hai is liye iska base 16 hota hai.
◼ Lekin agar hamare pas ek hexadecimal number h (21015)16 toh number h 21015 toh sabse pehla number h 2 wo 0-15 ki range m h. Ab dusra number h 1 wo bhi 0-15 ki range m h lekin 0-15 ki range m 10 bhi to h na to confusion ye h ki 1 ko m alag lu or 0 ko alag jo ki dono 0-15 ki range m h ya fir 1 or 0 ko combined lu 10 ye bhi 0-15 ki range m h same case 1 or 5 ke sath h ki ye 1 alag or 5 alag h ya fir combined h 15.
◼ Is problem ko solve krne k liye aya hai hexhadecimal me characters ka use or woh charater kya hai( A,B,C,D,E,F)
◼ Lekin ab ye bat aajati hai ki ye characters ham use kha krenge (0-9) tak ke numbers toh single digits hai or (10 – 15) tak ke numbers double digits hai toh jaise double digits aa jata hai toh wha ham characters use krnge kaise aiye dekhtey hai
◼ Single digits : 0,1,2,3,4,5,6,7,8,9
◼ Double digits : 
◼ agar ab hamare pas hexadecimal number h (21015)16 toh yha sab number seprate h 2 alag 1 alag 0 alag 1 alag 5 alag or agar hame 10 or 15 show karna h to number hoga (2AF) A=10 and F=15.
Example: (10DB9)16 ab pta chal rha hai ye hexadecimal number hai or 1 alag h 0 alag h D=13 B=11 or last h 9.
Note:- Jab kisi bhi number ka base 16 hota hai toh usko Hexadecimal Number boltey hai.

CONVERSION DECIMAL TO BINARY

Ab ek Table dekte h jo bohot useful h or easy bhi lekin sirf rough work ke liye

  Goes to Infinite     28     27     26     25     24     23     22     21     20  
  Get Twice Each Time     256     128     64     32     16     8     4     2     1  

◼ Ab hum yha ye dekh rahe h ki yha do row h uper wali row m 2 ki power h or niche wali row m ek number h.
◼ To ye kaise bani hum start karte h 2 se matlab ki base m 2 likh lenge or sabhi 2 par power likhenge.
◼ Power start hogi 0 se jo sabse rightmost 2 par lagegi or badti chalegi jaise start hogi 0, 1, 2, 3, 4, 5...... Infinite (matlab kabhi bhi end nahi hoga).
◼ Or niche wali row m start hoga 1 se kyo ki 20 ki value 1 hoti h or aage wala number apne piche wale ka double ho jayega.
◼ jaise pehle 1, fir 1 ka double 2, 2 ka double 4, 4 ka double 8, 8 ka double 16, or fir 16 ka double or aise hi double hota jayega.
◼ Now we are going to prove why the value of 20 = 1 ?
◼ Ab hum dekhte h ki 20 ki value 1 kyo hoti h.
◼ Or sirf 20 ki value 1 nahi hoti balki kisi bhi Natural number (1, 2, 3, 4, 5.....) ki power agar 0 h to uski value 1 hogi.
         20 = 1
         LHS (Left Hand Side) h 20    OR    RHS (Right Hand Side) h 1
         we take RHS 1
         =1
         =2/2    (i.e    2/2 = 1/1   and   1/1 = 1)
◼ (agar 4/2 hoga to solve karne par iski value 2 hogi aise hi 2/2 ko solve karne par uski value 1 hogi. To isi liye humne 1 ki jageh 2/2 likh diya.)
         =21/21    (i.e    21/21 = 2/2   and   2/2 = 1/1   and   1/1 = 1)
◼ (21/21 = 2/2 kaise   21 ki value 2 kaise dekho jab 22 ki value 4 hoti kyoki 2 ko 2 times likh kar uski apas m multiply karte h For Example 2 * 2 = 4 aise hi agar 23 ki value 8 hoti kyoki 2 ko 3 times likh kar uski apas m multiply karte h For Example 2 * 2 * 2 = 8 or same 24 ki value 16 hoti kyoki 2 ko 4 times likh kar uski apas m multiply karte h For Example 2 * 2 * 2 * 2 = 14 means jitni power utini bar 2 ko likho or apas m multiply kar do)
◼ (To aise hi jab 21 hogi to hum 2 ko sirf ek bar likhenge kyoki power 1 h or jab dusra number h hi ni to multiply kisese karenge kisi se bhi nahi for Example 2 = 2)
         =21 * 2-1    (i.e    21/21 = 21 * 2-1)
◼ (DIVISION SIGN "/" ke uper wale number ko numerator or niche wale number ko denominator kehte h.)
◼ (To jab bhi denominator yani niche wale number ko uper lejate h to agar usper power h to power ka sign opposite ho jata h jaise ki hamare case m hua niche +1 tha to uper jane ke baad -1 ho gaya or agar negative hoti to uper jane ke baad positive ho jati.)
◼ (Or niche wala number uper jane ke baad DIVISION ki jageh MULTIPLICATION ho jayega same hamne kiya.)
         =21 + ( -1 )    (i.e    21 * 2-1 = 21 + ( -1 ))
◼ (Jab bhi base same honge jaise ki hamare case m 2 ki power 1 multiply by 2 ki power -1 dono base same h 2 or 2 to hamesha powers apas m add ho jayegi isiliye 1 + ( -1 ) kiya.)
         =21 - 1
         =20
◼ (To Finally hame mila 20 jo ki hamara LHS tha)
         So, We have LHS = RHS Hence Proved
◼ (Same yehi dusre kisi bhi Natural Number ke sath hoga agar uski power 0 h to.)
         Now,
         21 = 2 = 2
         22 = 2*2 = 4
         23 = 2*2*2 = 8
         24 = 2*2*2*2 = 16
         25 = 2*2*2*2*2 = 32
         26 = 2*2*2*2*2*2 = 62
         27 = 2*2*2*2*2*2*2 = 128
◼ To Ab humne sikh liya. Ab hum dekhenge ki Decimal se Binary m kaise convert hota h
◼ We will Convert ()10 = ()2
◼ Matlab hume base 10 ko base 2 m convert karna h.
◼ Question :- Convert decimal to binary.
    (117)10 = (?)2
◼ Yha hume 117 Decimal number ko equivalent Binary number m convert karna h.
◼ Sabse pehle hum wahi table bana lenge jo humne uper dekhi thi Lekin sirf rough m.
◼ Start karenge page ke right side se sabse pehle 1 likh kar.
◼ Fir 1 ka double 2, 2 ka double 4, 4 ka double 8, or aage double karte jayenge.
   FisadDi_Image
◼ Kab tak karna h dekho humara decimal number h 117 to jaise hi double katre karte humari limit cross ho jaye hum ruk jayenge.
◼ Humara decimal number h 117 to jaise hi double katre karte hume 128 mila jo ki 117 se bada h to hum ruk jayenge 128 ko nahi lenge.
◼ Ab hum 64 ke niche 1 likh denge kyoki 64   117 se smaller h (64 ≺ 117).
◼ Aise hi 32 ke niche bhi 1 likh denge kyoki (64 + 32) = 96 ye bhi 117 se smaller h (((64 + 32) = 96) ≺ 117).
◼ Aise hi 16 ke niche bhi 1 likh denge kyoki (64 + 32 + 16) = 112 ye bhi 117 se smaller h (((64 + 32 + 16) = 112) ≺ 117).
◼ Lekin 8 ke niche 0 likhenge kyoki (64 + 32 + 16 + 8) = 120 jo ki 117 se bada h (((64 + 32 + 16 + 8) = 120) ≻ 117).
◼ Ab aata h 4 jiske niche 1 likhenge kyoki (64 + 32 + 16 + 4) = 116 jo ki 117 se smaller h (((64 + 32 + 16 + 4) = 116) ≺ 117).
◼ Lekin 2 ke niche 0 likhenge kyoki (64 + 32 + 16 + 4 + 2) = 118 jo ki 117 se bada h (((64 + 32 + 16 + 4 + 2) = 118) ≻ 117).
◼ Last and finally 1 ke niche 1 likhenge kyoki (64 + 32 + 16 + 4 + 1) = 117 jo ki 117 ke equal h or yahi hume karna h (((64 + 32 + 16 + 4 + 1) = 117) = 117).
◼ To bas hume yahi karna h ki jis number ke niche '1' likha h matlab ki wo wala number 'IN' h or jis number ke niche '0' likha h wo wala number 'OUT' h.

   FisadDi_Image

◼ To ab hume (117)10 = (1110101)2 ka conversion mil gaya lekin ye sirf rough work ke liye kyoki EXAM m aise marks nahi milenge.
◼ Lekin rough m ye karne ke baad ab exam m marks lene ke liye ye kam karenge kaise.
   FisadDi_Image
◼ Sabse pehle aisi ek table bana lenge jisme Left Side m 2 2 kyo binary m convert karna h or Top par 117 likh denge.
   FisadDi_Image
◼ Humara Binary number h (1110101)2 jaise image m dikh ra h waise hi likhenge.
   FisadDi_Image
◼ ((2 * 1) + 1) = 3 isiliye humne 3 likha.
◼ ((2 * 3) + 1) = 7 to hum uper 7 likh denge or same aise hi agar karte jayenge.
   FisadDi_Image

          ((2 * 1) + 1) = 3
          ((2 * 3) + 1) = 7
          ((2 * 7) + 0) = 14
          ((2 * 14) + 1) = 29
          ((2 * 29) + 0) = 58
          ((2 * 58) + 1) = 117
◼ Finally hame hamari table mil gayi or easy bhi h kyoki multiplication or addition Division se easy hota h.
◼ Finally ye table banane ke baad hum aapna result likh denge.
          (117)10 = (1110101)2

<-------------------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.