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18. Subtraction using 9's complement

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Computer Organization & Architecture

Subtraction using 9’s Complement

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 9’s complement nikalenge kyoki wo negative number hai.
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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.
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◼ Ab hum jaise hi 9’s complement nikal lenge toh isko hum M main add kar denge kyoki (-N) ka to humne 9’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 niche add kar denge jaisa image main diya hua hai.
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◼ Finally humara result aa gaya hai toh hum isko aise likh denge jaisa image main diya hua hai.
◼ Note : Agar M bada hai N se toh agar carry ata hai add karne par toh jo sabse left side main number hai hum usko niche add kar denge jaise upar example main kiya hua hai.

2.  (1213)10 – (2729)10 = (?)10

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◼ Sabse phele hum (1213)10 ko M maan lete hai or (2729)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 9’s complement nikalenge kyoki wo negative number hai.
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◼ Ab hum check karnge ki M or N dono number equal digits ke hai ki nahi toh humne dekha ki M or N dono equal digits ke hai jaisa image main diya hua 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.
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◼ Ab hum jaise hi 9’s complement nikal lenge toh isko hum M main add kar denge kyoki (-N) ka to humne 9’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 (1213) jo ki Positive number hai chota (small) hoga N (2729) se jo ki Negative number hai to add karne ke baad jo result aaya usse dobara se 9’s complement main convert karnge.
◼ Or kyoki Negative number bada hai Positive number se to jo Final Result hai wo bhi negative hi hoga isiliye (-1516)10 final answer hoga.
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◼ Finally humara result aagaya hai toh isko hum aise likhnge jaisa image main likha hua hai.
◼ Note : Agar Negative number ‘N’ bada hai Positive number ‘M’ se to add karne ke baad jo Result aayega usse dobara se 9’s complement main convert kar denge jaise upar example main kiya hua hai.

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