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8. Positional Numbering System Part 8 (Conversion Octal to Decimal, Binary & Hexadecimal with Fixed or Radix Point)

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Computer Organization & Architecture

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

1.Octal to Decimal

◼ Isme hum convert karnge base 8 ko base 10 main ()8 = ()10
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◼ Upar wali table se Octal se decimal me conversion karna bohot easy ho jayega to sabse pehle upar di hui table samajhte hai.
◼ Center me Point h jise Radix Point kehte h .
◼ Point ke left side me hamesha 8 ki power 0 se start hoga or aage baadhata jayge.
◼ Point ke right side m 8 ki power -1 se start hoga or aage negative me baadhata jayga.
◼ Ab 8 ki power 0 ki value 1 hoti hai.
◼ 8 ki power 1 ki value 8 hoti hai.
◼ 8 ki power 2 ki value 8 * 8 = 64.
◼ To agar power positive h to jitni bhi power h utni baar 8 likh kar multiply kar denge.
◼ Lekin jab power negative me aayegi tab ek easy trick hai.
◼ 8 ko hum 2 ki power 3 likh sakte h kyoki 23 = 2 * 2 * 2 = 8.
◼ Ab agar 8-1 hai to isse hum (23)-1 likh sakte hai or 3 * (-1) = -3.
◼ To jab bhi 2 ki power negative hoti h to waha hum 5 ko use karte hai.
◼ Jaise 8-1 = 2-3 , 5 * 5 * 5 = 125 or sabse aage point laga do to final answer hua 0.125 to 8-1 = 0.125.
◼ Same 8-2 = 2-6
◼ 2-6 = 2-3 * 2-3
◼ 0.125 * 0.125 = 0.015625 , to 8-2 = 0.015625 .
◼ Same aise hi aage bhi nikal lenge jo bohot easy hai.
◼ Ab ek example lete jisse ache se samahje aayga.
◼ Let's take an example
    (56.35)8 = (?)10
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◼ Hum dekh rhe hai ki yha par do number hai ek point ke left side main (56) or dusra point ke right side main (35) jaisa image main diya hai toh sabse phele point ke left side wale ko convert karnge.
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◼ Point ki left side m 80 se start karnge multiply karna.
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◼ Ab humne 8 ki power ki joh value hai usko likh kar multiply kiya hai jiska answer aya hai 46 jaisa image main diya hai.
◼ Ab point k right side 35 ko convert karnge.
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◼ Point ke right side ko convert karne ke liye hum 8-1 se start karnge jaisa image main kiya hai.
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◼ Ab hum dekh rhe hai ki 8 ki joh power minus main hai uski value rakh kar phir multiply karke humne answer nikal diya hai jaisa image main kiya hai.
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◼ Phir jaise hi point ke right and left dono side ko convert kar lenge to waise hi hum dono ko add kar denge jaisa image main kiya hai.
◼ Finally hum jo result aaya h usse likh denge.
    (56.35)8 = (46.453125)10

2.Octal to Binary

◼ Isme hum convert karnge base 8 ko base 2 main ()8 = ()2
◼ Let's take an example
    (56.35)8 = (?)2
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◼ Isko sabse phele hum distance main likh lenge jaisa image main likha hai.
◼ Fir sabhi number ko 3 bits Binary main convert karnge.
◼ Binary main convert karne ke liye table ka ‘ 4 2 1 ‘ lenge.
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◼ Binary main convert hone ke baad sabhi binary bits ko mila kar likh denge or jha point h waha point laga denge.
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◼ Finally jo result aaya h usse likh denge jaise image main dikhaya hai.
    (56.35)8 = (101110.011101)2

2.Octal to Hexadecimal

◼ Isme hum convert karnge base 8 ko base 16 main ()8 = ()16
◼ Sabse phele Octal ko convert karnge Binary main jaise hi Binary main convert ho jayega waise hum usko Hexadecimal main convert kar denge.
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◼ Let's take an example
    (56.35)8 = (?)16
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◼ Isko bhi same waise hi karenge jaise abhi upar kiya h kyoki Octal se Binary main same waise hi convert karte hai jaise upar kia hai or yaha to example bhi same hi hai to hum direct aapna answer likh lenge.
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◼ Ye Binary main kaise convert hua iske liye upar Octal se Binary conversion wala section dekho.
◼ Jaise Binary main convert kar lenge fir sab ko sath main likh lenge jaisa image main likha hai or ab isko Hexadecimal main convert karnge.
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◼ Lekin jab hum Binary se Hexadecimal m convert karte h to Binary bits ko hum 4-4 ke pair m divide karte h.
◼ To jo bits point ke left side m h unhe hum jaha se start from here wala arrow h waha se divide karna start karnge or point ke right side wali bits ko jaha arrow h waha se divide karna start karge.
◼ To sabse pehle point k left side wali bits ko divide karnge.
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◼ Ab 4-4 bits main divide ho gaya lekin dekh rhe hai ki last wale group m sirf 2 hi bits h to usse bhi 4 bits m karne ke liye ‘1 0’ ke pehle 2 zero’s laga denge jaisa image main kiya hai.
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◼ 4-4 bits m divide karne ke baad table ka ‘ 8 4 2 1 ‘ lete h Hexadecimal main convert karne k liye fir sabhi group ko ek ek karke table use karke convert karnge jaisa image main kiya hai.
◼ Jha 14 aaya hai waha E isliye liya hai kyoki Hexadecimal main double digit number aate hi usko hum ek Character de dete hai jaisa image main kiya hai.
◼ 10 ko ‘A’ , 11 ko ‘B’ , 12 ko ‘C’ , 13 ko ‘D’ , 14 ko ‘E’ or last 15 ko ‘F’ se denote karte h.
◼ To humara left side wali bits Hexadecimal m convert ho gayi lekin abhi right side wali bits bachi h to usse convert karte h.
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◼ Ab 4-4 bits main divide karnge jha se start from here likha hai wha se jaisa image main kiya hai.
◼ Lekin last m sirf 2 hi bits h to use 4 bits karne k liye ‘0 1 ’ ke aage 2 zero’s laga denge jaisa image m kiya h.
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◼ Hexadecimal main convert karne k liye table ka ‘ 8 4 2 1 ‘ lenge ek ek karke sabhi groups ko convert karnge jaisa image main kiya hai.
◼ To ab right side wali bits bhi Hexadecimal m convert ho gayi.
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◼ Ab isko hum aise likhe denge jaise Hexadecimal main convert ho jayega jaisa image main likha hai.
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◼ Finally jo result aaya h usse likh denge jaise image main dikhaya hai.
    (56.35)8 = (2E.74)16

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