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19. Subtraction using 10's complement

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Computer Organization & Architecture

Subtraction Using 10’s Complement

◼ Note : 10’s Complement nikalne se phele humesha 9’s complement nikalte hai jaise hi 9’s Complement nikal jayega usme 1 add kar denge 10’ s Complement main convert karne ke liye.

1.  (72532)10 – (3250)10 = (?)10

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◼ Sabse phele hum (72532)10 ko M maan lete hai or (3250)10 ko N maan lete hai jaisa image main diya hua hai.
◼ Jab minus N ko brackets main le lete hai to by default + sign lag jayega.
◼ Ab (-N) ka 10’s complement nikalenge kyoki wo negative number hai.
◼ Lekin 10’s complement main convert karne se pehle 9’s complement main convert karenge.
◼ Jaise hi 9’s complement main convert ho jayega fir usme 1 add karke 10’s complement main convert kar denge.
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◼ Ab hum check kar rahe hai ki M or N equal digits ke hai ya nahi toh hum (-N) ko 9’s Complement main change karne se phele equal kar lenge toh N ko 5 digits main benane ke liye bilkul left main 0 likh denge jaisa image main likha hai.
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◼ ‘N’ ko 9’s complement main convert karne ke liye ‘N’ ki har ek digit ko 9 main se minus kar denge.
◼ Humne 9’s complement nikal liya hai ab 10’s complement nikalenge.
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◼ 10’s complement main convert karne ke liye jo 9’s complement aaya hai usme 1 add kar denge.
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◼ Ab hum jaise hi 10’s complement nikal lenge toh isko hum M main add kar denge kyoki (-N) ka to humne 10’s complement nikal liya or ab sirf ‘+’ sign bacha jaisa image main diya hua hai.
◼ Lekin abhi final result nahi aya hai.
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◼ Ab add karne par 6 digits aaya hai lekin humare pass dono number 5 digits ke hai toh extra digits aaya hai to jo sabse left side wala number hai usse hum discard kar denge jaisa image main diya hua hai.
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◼ Finally humara result aagaya hai isko hum aise likh denge jaisa image main diya hua hai.
     (72532)10 - 3250)10 = (69282)10

2.  (3250)10 – (72532)10 = (?)10

  FisadDi_Image
◼ Sabse phele hum (3250)10 ko M maan lete hai or (72532)10 ko N maan lete hai jaisa image main diya hua hai.
◼ Jab minus N ko brackets main le lete hai to by default + sign lag jayega.
◼ Ab (-N) ka 10’s complement nikalenge kyoki wo negative number hai.
◼ Lekin 10’s complement main convert karne se pehle 9’s complement main convert karenge.
◼ Jaise hi 9’s complement main convert ho jayega fir usme 1 add karke 10’s complement main convert kar denge.
  FisadDi_Image
◼ Ab hum check kar rahe hai ki M or N equal digits ke hai ya nahi toh hum (-N) ko 9’s Complement main change karne se phele equal kar lenge toh M ko 5 digits main benane ke liye bilkul left main 0 likh denge jaisa image main likha hai.
  FisadDi_Image
◼ ‘N’ ko 9’s complement main convert karne ke liye ‘N’ ki har ek digit ko 9 main se minus kar denge.
◼ Humne 9’s complement nikal liya hai ab 10’s complement nikalenge.
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◼ 10’s complement main convert karne ke liye jo 9’s complement aaya hai usme 1 add kar denge.
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◼ Ab hum jaise hi 10’s complement nikal lenge toh isko hum M main add kar denge kyoki (-N) ka to humne 10’s complement nikal liya or ab sirf ‘+’ sign bacha jaisa image main diya hua hai.
◼ Lekin abhi final result nahi aya hai.
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◼ Jab bhi M (3250) jo ki Positive number hai chota (small) hoga N (72532) se jo ki Negative number hai to add karne ke baad jo result aaya hai usse dobara se pehle 9’s complement main convert karke 10’s complement main convert kar denge.
◼ Or kyoki Negative number bada hai Positive number se to jo Final Result hai wo bhi negative hi hoga isiliye (-69282)10 final answer hoga.
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◼ Finally huamara result aagaya hai toh isko hum aise likh denge jaisa image main diya hua hai.
◼ Note : Agar Negative number ‘N’ bada hai Positive number ‘M’ se to add karne ke baad jo Result aayega usse dobara se pehle 9’s complement main convert karke fir 10’s complement main convert kar denge jaise upar example main kiya hua hai.

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