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6. Positional Numbering System Part 6 (Conversion Decimal to Binary, Octal & Hexadecimal with Fixed or Radix Point)

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Computer Organization & Architecture

1. Conversion From Decimal to Binary, Octal and Hexadecimal with Fixed or Radix point

◼ Main ye betaya tha ki Decimal se Binary main kaise convert kartey hai lekin agar numbr k bich main point laga ho to hum isko kaise convert karnge aiye dekhtay hai.
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◼ Agar kisi bhi number k bich point lega ho toh hum Computer Organization main isko Fixed ya fir Radix Point boltey hai.

1.Decimal to Binary

◼ Let's take an example
    (40.50)10 = (?)2
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◼ Hum yha dekh rhe hai ki yha par do number hai fixed point k left main 40 hai or fixed point k right main 50 hai hum dono ko alag alaga convert karnge toh sabse phele bat kartey hai 40 ki.
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◼ Ab isko hum jaise convert kartey the table le kar waise hi karnge toh dekh rhe h ki 64 joh hai woh 40 se bada hai toh woh bahar ho gaya jaise 40 binary main convert ho jaye usko likh diya lekin abhi complete ni hua hai ab hum convert karnge fixed point k right wale number 50 ko.
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◼ Ye hum sirf point ke right m jo number h usi ke sath karenge .ab 50 ko convert karnge lekin table lekr ni multiply karke 2 se, hum 2 se multiply isliye kr rhe hai kuki binary ka base 2 hota hai aur stop kar denge jaise 0 ata hai.
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◼ Finally hum result likh denge jaise image main likha hai.
    (40.50)10 = (101000.1)2

2.Decimal to Octal

◼ Isko convert karnge base 10 se base 8 main ()10 = ()8
◼ Let's take an example
    (30.65)10 = (?)8
◼ Main ek chiz betaya tha ki agar Decimal se Octal main convert kar rhe hai toh sabse phele Decimal se Binary main convert kartey hai jaise hi Binary main convert ho gaya toh hum usko Octal main convert kar denge.
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◼ Yha bhi hum dekh rhe hai ki yha bhi two number hai ek Radix point k left main joh 30 hai and dusra Radix point k right main job 65 hai aiye ab conver kartey hai.
◼ Sbase phele convert karnge radix point k left main joh number hai 30 ko.
◼ Isko hum table main jaise convert kartey the waise hi karnge lekin sabse phele hum Decimal se Binary main convert karnge.
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◼ Table ka 32 joh h who toh 30 se bada hai toh woh table se bahar ho gaya toh hum dekh rhe hai ki 30 binary main covert ho gaya hai (11110)2 ab isko hum convert karnge Octal main jaisa image main kiya hai.
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◼ Octal main convert karne k liye hum (11110)2 ko 3-3 bits main divide karnge lekin hum dekh rhe hai ki last main 2 bits hi hai isko 3 bits main benane k liye bilkul left side main 0 add kar denge jaisa image main kiya hai.
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◼ Humne isko Octal main convert kar liya hai jaisa image main kiya hai.
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◼ Humara 30 Octal m convert ho gaya jaisa image main likha hai lekin abhi kevel radix point k left wala number convert hua hai ab radix point k right wala number 65 ko convert karnge.
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◼ Ab radix point k baad wala number convert karnge Octal main to isko multiply karnge 8 se kuki Octal ka base 8 hai or radix point k baad wale number ko hum multiply karke convert kartey hai.
◼ Hum dekh rhe hai ki last main pura complete answer ni nikala hai kuki ye repeat ho raha h hum isko aise hi end kar denge or last main dot dot laga kar likh denge jaisa image main likha hai.
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◼ Jaise humne convert kr liya toh hum isko aise likh denge jaisa image main likha hai.
◼ Finally humara resul aa gaya toh hum aise likh denge.
    (30.65)10 = (36.51463…)8

3.Decimal to Hexadecimal

◼ Isme hum convert karnge base 10 se base 16 main ()10 = ()16
◼ Decimal se Hexadecimal main convert karne k liye hum sabse phele convert kartey hai Decimal se Binary main jaise Binary main convert ho jayega waise hi convert kar denge Hexadecimal main.
◼ Let's take an example
    (40.50)10 = (?)16
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◼ Yha bhi hum dekh rhe hai ki yha bhi two number hai ek Radix point k left main joh 40 hai and dusra Radix point k right main job 50 hai or dono ko hum alag alag convert karnge.
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◼ Hum dekh rhe hai ki 64 bada hai 40 se toh 64 table main nahi ayega or 40 ko Binary main convert kar liya hai ab isko Hexadecimal main convert karnge.
◼ Yaha hum binary number ko 4-4 bits m divide kar lenge.
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◼ Jaise hi Binary main convert ho jayga usko hum Hexadecimal main convert karnge or Hexadecimal main convert karne k liye hum isko 4-4 bits main divide karnge jha se start karne ko likha hai wha se divide karnge jaisa image main kiya hai.
◼ Humne dekha ki last main kevel 2 bits becha hai toh usko hum 4 bits main karnge uske liye last main bilkul last main two 0 add kar denge jaise image main kiya hai.
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◼ Ab isko hum Hexadecimal main convert karnge uske liye table ka 8 4 2 1 lenge 4 bits k liye phr convert karnge jaisa image main kiya hai.
◼ Radix point left wala number hexadecimal main convert ho gaya hai ab Radix point k right wala number 50 ko convert karnge.
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◼ Hum yha 16 se multiply isliye kar rhe hai kuki hecadecimal ka base 16 hota hai or point k right wale number ko convert karne k liye hum multiply hi kartey hai jaisa image main kiya hai.
◼ Jaise hi pura convert kar lenge hexadecimal main toh isko aise likh denge jaisa image main likha hai.
◼ Finally humara result aa gaya isko hum aise likh denga.
    (40.50)10 = (28.8)16

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