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5. Positional Numbering System Part 5 (Conversion Hexadecimal to Decimal, Binary & Octal)

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Computer Organization & Architecture

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


  1. Conversion from Hexadecimal to Decimal:-

◼ Isme hum convert krenge base 16 ko base 10 main ()16 = ()10.
◼ Jaise humne Binary se decimal main convert krne k liye base 2 use kiya tha, octal se decimal main convert krne k liye base 8 use kiya tha waise hi hum hexadecimal se decimal main convert krne k liye base 16 use krnge.
    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 162 = 16 * 16 = 256 hota hai jo hum 16 ki 16 me ek bar multiply kar ke dekh sakte h.
  ◼ Agar 163 = 16 * 16 * 16 = 4096 hota hai 16 ko 3 bar multiply karke.
  ◼ Agar 164 = 16 * 16 * 16 * 16 = 65536 hota hai 16 ko 4 bar multiply karke.
  ◼ Isko krne se answer to nikl jayega lekin time lagega or pareshani bhi hogi .
◼ Ab jaise ek binary or octal ka table betaya tha waise hi hexadecimal ka table betane ja rha jo bohot easy h.
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◼ 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 163 chahiye to m 16 par jo power h yani 3 ko 4 se multiply kar dunga 3 * 4 = 12.
  ◼ To hum 13 bar double kate jayenge 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096 to 3 * 4 = 12 (212 = 163 = 4096).
  ◼ Aise hi agar mujhe 164 chahiye to m 4 ko 4 se multiply kar denge 4 * 4 = 16 kyoki power m 4 h.
  ◼ To is bar hum 17 bar double karte jayenge jab hamara pehle answer aya 12 to humne 13 bar double kiya or jab hamara answer aya 16 to hum 17 bar karenge matlab answer m 1 ko add kar denge 16 + 1 = 17 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, 13, 14, 15, 16, 17 ye sab 2 ke uper power h.
  ◼ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384 , 32768 , 65536 to 4 * 4 = 16 (216 = 164 = 65536).
  ◼ Ye sabhi aapko aapki ungali par kar loge bohot easy h.
  ◼ 161 = 16 hota hai kyoki 1 * 4 = 4 .
  ◼ 24 = 16
  ◼ 162 = 256 hota hai kyoki 2 * 4 = 8 .
  ◼ 28 = 256
  ◼ 163 = 4096 hota hai kyoki 3 * 4 = 12 .
  ◼ 212 = 4096
  ◼ 164 = 65536 hota hai kyoki 4 * 4 = 16
     simply 4096 * 2 * 2 * 2.
  ◼ 216 = 65536
  ◼ Hum dakh rhe hai ki easily calculation ho rha hai agar aise use kr rhe hai toh.
◼ Let's take an example
    (179)16 = (?)10
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◼ Sabse phele aise likh denge jaise image main liklha hai.
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◼ Uske baad multiply ka sigh lega denge jaise image main legaya hai.
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◼ Phir multiply k baad base 16 ki power lega denge jaise image main legaya hai.
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◼ Phir usk baad addition ka sign lega denge jaise image main legaya hai.
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◼ Uske baad sbhi ki value likh kar result nikal denge.
       (179)16 = (377)10
◼ Finally humara result aa gaya toh aise hi hum exam main likhenge.
  2. Conversion from Hexadecimal to Binary:-
◼ Isme hum convert kernge base 16 ko base 2 main ()16 = ()2
◼ Let's take an example
    (179)16 = (?)2
◼ Phele hum jaise image main likha hai 1 7 9 waise likh lenge.
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◼ Sabse phele 9 ko 4 bit main convert krenge jaise image main kiya hai.
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◼ Uske baad 7 ko 4 bit main convert krnge jaise image main kiya hai.
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◼ Phir hum 1 ko 4 bit Binary main convert krenge jaise image main kiya hai.
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◼ Jaise Binary main convert kr lenge phir usk baad hum isko sath main likh denge jaise image main likha hai lekin usi sequence m jisme hexa m likha h 1 ka binary sabse pehle fir 7 ka binary or last m 9 ka binary likhenge.
◼ Finally humara result aa gaya
       (179)16 = (000101111001)2
  3. Conversion from Hexadecimal to Octal :-
◼ Isme hum convert krety hai base 16 ko base 8 main ()16 = ()8
◼ Sabse phele hum Hexadecimal ko convert krnge Binary main phir jaise hi Binary main convert ho jayega uske baad hum usko Octal main convert kr denge.
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◼ Ye same waise hi karenge jaise humne uper kiya Hexcimal ko Binary convert kiya.
◼ Let's take an example
    (A2C)16 = (?)8
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◼ Sabse phele hum dakh rhe hai ki example main A or C aya hai toh uska matlab h ki hexadecimal main jaise double digit ata hai toh hum usko digits main na likh kr charater main likhtey h toh A = 10 and C = 12 hota hai jaise image main likha hai waise likh denge.
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◼ Sabse phele hum 12 ko 4 bit binary main convert krnge or 4 bit main isliye krnge kuki hum hexadecimal se convert kr rhe yha.
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◼ Ab hum 2 ko 4 bit Binary main convert krnge jaise image main kiya hai.
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◼ Ab hum 10 ko 4 bit Binary main convert krnge jaise image main kiya hai.
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◼ Jb sbhi number binary main convert ho jayega toh sab ko sath main likh denge lekin usi sequence m jisme hexa m likha h A yani 10 ka binary sabse pehle fir 2 ka binary or last m C yani 12 ka binary likhenge.
◼ Ab humko jo Binary number mila h use hum Octal main convert krnge.
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◼ Jaise hi Binary number main convert kr denge uske baad hum isko octal main convert krne k liye hum Binary Number ko 3-3 bit main divide krna hoga hum 3-3 bit main divide isliye kr rhe hai kuki ab humko octal main convert krna hai.
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◼ Ab jha se start from here likha hai wha se octal main bari bari convert krna start krnge octal main convert krne k liye hum 4 2 1 binary table ka use krnge.
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◼ Ab 101 ko hum octal main convert krnge jaise image main kiya hai.
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◼ Ab Hum 000 ko Octal main convert krnge jaise image main kiya hai.
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◼ Ab last main hum 101 ko octal main convert krnge jaise image main kiya hai.
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◼ Jha se start from here likha hai wha se hum result likh denge jaise image main likha hai.
◼ Finally humara hexadecimal se octal main convert ho gya.
       (A2C)16 = (5054)8

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