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3. Positional Numbering System Part 3 (Conversion Binary to Decimal, Octal & Hexadecimal)

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Computer Organization & Architecture

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


  1. Conversion from Binary to Octal

◼ base 2 ko base 10 main convert Isme hum krte hai ()2 = ()10.
◼ Let's take an example
◼ (1101011)2 = (?)10
Toh sabse phele rough work kernge bina rough work kiye humara question solve ni hoga

  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  

◼ Sabse phele table jo benaya tha who use krenge.
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◼ Ab kya krenge jaise table benaya tha uske upar jo binary number diya hua hai (1101011) wo likh denge jaise table main likha hua hai.
◼ Phir binary number or two ki power k bich multiply (*) ka sign hai usko lega denge jaise table main bena hua hai.
◼ Ab multiply ka sign legane k bad sbhi number k bich addition(+)ka sign lega denge jaise table me bena hua hai.
◼ Or fir uper se niche or left se right likhenge jaise sabse pehle left m uper likha h 1 uske niche multiply (*) ka sign or uske niche 26 h.
◼ Fir right m addition(+)ka sign .
◼ To 1 * 26 + 1 * 25 or aise hi aage likenge jaise uper dikhaya bhi h.
  Lekin yeh humara rough kam tha ab number exam main lane k liye yeh kam krnege lekin han bina rough kam kiye isko aise jaise krne ja rha wo kam ni hoga.
◼ Phir jha se start from these side likha hua hai usko likh denge.
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◼ Phir jaise image main likha hai 26 = 64 hota hai toh 1 * 64 kr diya.
◼ Jaise image m likha hai ki sbhi power ki value kya hota h wo likh denge.
◼ Finally hum ye kam krnge jisse humara result aa jayega
    1 * 64 + 1 * 32 + 0 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 * 1
    64 + 32 + 0 + 8 + 0 + 2 + 1 = 107
◼ Result aa gya ye lekin isko likhenge kaise
    (1101011)2 = (107)10
  2. Conversion from Binary to Octal
◼ Isme hum base 2 ko base 8 main convert krenge ()2 = ()8
◼ Let's take an example
    (101101)2 = (?)8
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◼ Ab isko hum 3-3 bit me divide kr denge.
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◼ Divide krne k baad hum octal main 3 bits k liye table ka 4 2 1 use krtey hai toh isko use krnge or joh 3-3 bits m divide kiya hai usko likh denge jaise image main likha hai waise solve kr denge.
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◼ Final result jo image me aya waise likh denge
    (10101)2 = (55)8
  3. Conversion from Binary to Hexadecimal
◼ Isme hum base 2 ko base 16 main convert krenge ()2 = ()16
◼ Let's take an example
    (1101101)2 = (?)16
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◼ Jo yeh binary number (1101101) hai isko hum 4-4 bits me divide kar denge.
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◼ Hum dakhe rhe hai ki left most side main kevel 3 bits hai isko hume 4 bits me banana hoga uske liye left most bit main ek zero(0) legana hoga jaise image main kiya hai waise kr denge.
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◼ Jaise 4 bits main divide kar diya h waise isko hexadecimal me convert kar denge lekin isko hexa decimal main convert krne k liye hum table ka 8 4 2 1 use krnge jaise image main likha hai.
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◼ Finally humara result aa gaya jha se start from this side likha hai wha se aise likh kr result likhg denge
    (1101101)2 = (6D)16

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