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9. Positional Numbering System Part 9 (Conversion Hexadecimal to Decimal, Binary & Octal with Fixed or Radix Point)

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Computer Organization & Architecture

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

1.Hexadecimal to Decimal

◼ Isme hum convert karnge base 16 ko base 10 main ()16 = ()10
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◼ Upar wali table se Hexadecimal 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 main hamesha 16 ki power 0 se start hoga or aage positive main baadhata jayge.
◼ Point ke right side main 16 ki power -1 se start hoga or aage negative main baadhata jayga.
◼ Ab 16 ki power 0 ki value 1 hoti hai.
◼ 16 ki power 1 ki value 16 hoti hai.
◼ 16 ki power 2 ki value 16 * 16 = 256.
◼ To agar power positive h to jitni bhi power h utni baar 16 likh kar multiply kar denge.
◼ Lekin jab power negative me aayegi tab ek easy trick hai.
◼ 16 ko hum 2 ki power 4 likh sakte h kyoki 24 = 2 * 2 * 2 * 2 = 16.
◼ Ab agar 16-1 hai to isse hum (24)-1 likh sakte hai or 4 * (-1) = -4.
◼ To jab bhi 2 ki power negative hoti h to waha hum 5 ko use karte hai.
◼ Jaise 16-1 = 2-4 , 5 * 5 * 5 * 5 = 625 or 2 ki power main -4 hai to jo answer aaya usse 4 digits main karke sabse aage point laga do to final answer hua 0.0625 ; 16-1 = 0.0625.
◼ Same 16-2 = 2-8
◼ 2-8 = 2-4 * 2-4
◼ 0.0625 * 0.0625 = 0.00390625 ; 16-2 = 0.00390625.
◼ Same aise hi aage bhi nikal lenge jo bohot easy hai.
◼ Ab ek example lete jisse ache se samahj aayga.
◼ Let's take an example
    (A2.C4)8 = (?)10
◼ Ab aap ye soch rhe honge ki ye A or C kya hai toh sabse phele ye clear karte hai ki Hexadecimal main jaisa ki betaya tha 0 se 9 tak single digit chalta hai agar double digit aajaye toh jaise 10 se 15 isko character de dete hai. so A = 10 and C = 12.
◼ 10 ko ‘A’ , 11 ko ‘B’ , 12 ko ‘C’ , 13 ko ‘D’ , 14 ko ‘E’ or last 15 ko ‘F’ se denote karte h.
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◼ Hum dekh rhe hai ki yha par do number hai ek point ke left side main (A2) or dusra point ke right side main (C4) jaisa image main diya hai toh sabse phele point ke left side wale ko convert karnge.
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◼ Hum kya kar rhe isme ki point k left side main 16 ki power 0 se start hota hai toh jaise image main diya hai waise likh lenge.
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◼ Ab humne 16 ki power ki joh value hai usko likh kar multiply kiya hai jiska answer aya hai 162 jaisa image main diya hai.
◼ Ab point k right side C4 ko convert karnge.
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◼ Point ke right side ko convert karne ke liye hum 16-1 se start karnge jaisa image main kiya hai.
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◼ Ab hum dekh rhe hai ki 16 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.
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◼ Finally hum jo result aaya h usse likh denge.
    (A2.C4)16 = (162.765625)10

2.Hexadecimal to Binary

◼ Isme hum convert karnge base 16 ko base 2 main ()16 = ()2
◼ Let's take an example
    (A2.C4)16 = (?)2
◼ Sabse phele A or C ki value likh lete hai A = 10 and C = 12.
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◼ Isko sabse phele hum distance main likh lenge jaisa image main likha hai.
◼ Fir sabhi digits ko 4 bits Binary main convert karnge.
◼ Binary main convert karne ke liye table ka ‘ 8 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.
    (A2.C4)16 = (10100010.11000100)2

2.Hexadecimal to Octal

◼ Isme hum convert karnge base 16 ko base 8 main ()16 = ()8
◼ Sabse phele Hexadecimal ko convert karnge Binary main jaise hi Binary main convert ho jayega waise hum usko Octal main convert kar denge.
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◼ Let's take an example
    (A2.C4)16 = (?)8
◼ Sabse phele A or C ki value likh lete hai A = 10 and C = 12.
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◼ Isko bhi same waise hi karenge jaise abhi upar kiya h kyoki Hexadecimal 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 hai kaise hua iske liye upar Hexadecimal 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 Octal main convert karnge.
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◼ Lekin jab hum Binary se Octal main convert karte h to Binary bits ko hum 3-3 ke pair main 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 3-3 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 3 bits karne k liye ‘1 0’ se pehle ek 0 laga denge jaisa image m kiya h.
◼ 3-3 bits main divide karne ke baad table ka ‘ 4 2 1 ‘ lete h Octal main convert karne k liye fir sabhi group ko ek ek karke table use karke convert karnge jaisa image main kiya hai.
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◼ To humara left side wali bits Octal main convert ho gayi lekin abhi right side wali bits bachi h to usse convert karte hai.
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◼ Ab 3-3 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 3 bits karne k liye ‘0 0 ’ ke aage ek 0 laga denge jaisa image m kiya h.
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◼ Octal main convert karne k liye table ka ‘ 4 2 1 ‘ lenge ek ek karke sabhi groups ko convert karnge jaisa image main kiya hai.
◼ To ab right side wali bits bhi Octal main convert ho gayi.
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◼ Ab isko hum aise likhe denge jaise Octal 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.
    (A2.C4)16 = (242.610)8

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