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14. 1's and 2's complement

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Computer Organization & Architecture

1's and 2's complement

1.   1's complement

◼ Subtract each bit by 1 is one Complement.
◼ Ab jaise main ek chota sa example lekar betata hu .
◼ Is image main hum jo niche bits hai unhe subtract kar rahe hai 1 se jaisa ki image main diya hua hai.
◼ Let's take an example
◼ Find 1’s complement of ‘1001’
◼ By rule kaise kartey hai wo dekhtey hai
◼ Ab hum sabhi bits ko 1 se subtract kar denge toh jo result aaya hai wo 1’s complement hai jaisa image main diya hua hai.
◼ Ye to by rule hua ab ek easy trick hai 1’s complement nikalne ki wo dekhte hai.
◼ Lekin exam main hum by rule hi karenge jaise upar kiya.
◼ Isme hume sabhi bits ko 1 se subtract karne ki jaroorat nahi hai.
◼ Isme hum ‘1’ ke place par ‘0’ or ‘0’ ke place par ‘1’ likh denge jaisa image main kiya hai.
◼ Let’s take another example
◼ Find 1’s complements of ‘11.1101’
◼ Ab hum har ek bit ko 1 se subtract kar rhe hai jaisa image main diya hua hai.
◼ Jaise hi subtract kar lenge toh jo result ayega hum isko aise likh lenge jaisa image main likha hai.

2.   2's complement

◼ 2’s complement main convert karne ke liye sabse phele hum 1’s complement main convert karnge jaise hi 1’s complement main convert ho jayega uske baad hum 2’s complement main convert karnge.
◼ 2’s Complement main convert karne ke liye hum jab 1’s complement main convert kar lete hai tab isme hum 1 ko add kartey hai.
◼ Let’s take an example
◼ convert (1111001) into 2’s complement
◼ To convert (1111001) in 2’s complement we have step let’s see
◼ Step 1 -> We have to first convert (1111001) into 1’s complement
◼ By rule we have 1’s complement
◼ Abhi sirf 1’s complement aaya ahi jaisa image main diya hua hai.
◼ Ab hum 2’s complement main convert karne ke liye isme 1 add karnge.
◼ Step 2 -> Now we convert (1111001) into 2’s complement
◼ Finally humara result aa gaya hai ab isko aise likhnge jaisa image main likha hua hai.


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