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20. Signed Integer Representation

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Computer Organization & Architecture

Signed Integer Representation

◼ Signed Integer Representation ko hum Signed Integer Number bhi boltey hai.
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◼ Sabse phele baat kartey hai Integer kya hota hai, Integer minus infinite se start hota hai or plus infinite tak chalta hai jaisa image main diya hua hai.
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◼ Signed kya hota hai ab uski baat kartey hai, Minus(-) and plus(+) hota hai wahi signed hota hai jaisa image main diya hua hai.
◼ Representation matlab dikhana (show karna) Signed Integer ko.
◼ Signed Integer Representation ke 3 part hote hai : -
   ◼ i. Signed Magnitude Representation.
   ◼ ii. Signed 1’s Complement Representation.
   ◼ iii. Signed 2’s Complement Representation.
◼ 1’s Complement and 2’s Complement ke bare main hum jantey hi hai toh Signed 1’s Complement and Signed 2’s Complement Representation wahi hota hai ab baat kartey hai ki Signed Magnitude Representation kya hota hai.

A. Signed Magnitude Representation :-

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◼ Jaise humne 8 bits liya hai usme 1 bit joh hota hai woh Signed Magnitude Representation hota hai jaisa image main diya hua hai.
◼ Ab baat kartey hai ki Signed Magnitude Representation ko represent kaha karety hai.
◼ Humne 8 boxes liya kyoki yaha par 8 bits hai humare pass or phela bit joh hai Signed bit hai jaisa ki image main diya hai or Signed bit agar ‘1’ hai to minus (‘-‘) hota hai or agar ‘0’ hai to plus (‘+’) ke liye hota hai or joh bachi hui boxes hai woh Integer number ke liye hoga to total 8-bits ko mila kar Signed Integer Representation hota hai jaisa image main diya gaya hai.
◼ 1. Let’s take an example
◼ Represent +8 into Singed Magnitude ?
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◼ Sabse phele 8 ko hum binary main likhenge jo hai ‘1000’ jaisa image main diya hua hai.
◼ Ab hum plus(+) sign ko ‘0’ lekhenge or 8 ka ‘1000’ hai lekin hum dekh rahe hai 8 or plus ko mila kar kevel 5 bits hua hai 8 bits main karne ke liye sign bit ke baad or ‘1000’ ke pehle three zero’s laga denge jaisa image main kiya hai.
◼ + 8 ko humne boxes main Represent kiya hai toh phela bit joh hai woh signed bit hai jo plus hai or others bits number 8 hai jaisa image main diya hua hai.
◼ 2. Let’s take an another example
◼ Represent – 50 into Signed Magnitude ?
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◼ Sabse phele 50 ko hum binary main likhenge jo hai ‘110010’ jaisa image main diya hua hai.
◼ Ab hum minus(-) sign ko ‘1’ lekhenge or 50 ka ‘110010’ hai lekin hum dekh rahe hai 50 or minus ko mila kar kevel 7 bits hua hai 8 bits main karne ke liye sign bit ke baad or ‘110010’ ke pehle ek zero laga denge jaisa image main kiya hai.
◼ - 50 ko humne boxes main Represent kiya hai toh phela bit joh hai woh signed bit hai joh minus hai or others bits 50 number hai jaisa image main diya hua hai.
◼ 3. Let’s take an another example
◼ Represent 11101011 into 8 bits ?
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◼ Joh phela bit hai woh sign bit hai jaisa image main diya hua hai.
◼ Lekin ab iska humko decimal number likhna hai toh kaise likhnge aiye dekhtey hai.
◼ Kyoki pehla bit to sign bit hai to baki bachi hui 7 bits number hai jise hum Decimal number main convert karnge.
◼ Decimal number main convert karne ke liye Table ka ‘ 64 32 16 8 4 2 1’ use karnge or jiske bhi niche ‘1’ likha hai usse add kar lenge or jis ke niche ‘0’ likha hai usse add nahi karnge jaisa image main kiya hai.
◼ Ab kyoki 1st bit main 1 likha hai to matlab minus (-) sign hua.
◼ 64 + 32 + 8 + 2 + 1 = 107 kyoki Table ke inhi numbers ke niche 1 likha hai.
◼ Final answer hua (-107)10 jaisa image main diya hai.
◼ Note : Abhi tak humne sirf Signed Magnitude main kaise represent karte hai wo dekha ab baat karte hai ki agar Singed Integer main Represent karna ho to kaise karnge. Signed Interger Representation karte hua agar diya hua number Negative hai to usse pehle hum Signed Magnitude main karnge or fir uske baad Signed 1’s complement main convert karnge uske baad finally usse Signed 2’s complement main convert karnge.
◼ 1. Let’s take an example
◼ Represent + 49 and – 49 into Signed Integer ?

Signed Magnitude :-

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◼ Sabse phele 49 ko hum binary main likhenge jo hai ‘110001’ jaisa image main diya hua hai.
◼ Ab hum plus(+) sign ko ‘0’ lekhenge or 49 ka ‘110001’ hai lekin hum dekh rahe hai 49 or plus ko mila kar kevel 7 bits hua hai 8 bits main karne ke liye sign bit ke baad or ‘110001’ ke pehle ek zero laga denge jaisa image main kiya hai.
◼ +49 ko humne boxes main Represent kiya hai toh phela bit joh hai woh signed bit hai jo plus hai or others bits 49 number hai jaisa image main diya hua hai.
◼ +49 Positive number hai isiliye hum +49 ka Signed 1’s Complement nahi nikalge or na hi Signed 2’s Complement nikalnge.

Ab – 49 ko solve karnge.

Signed Magnitude :-

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◼ Sabse phele 49 ko hum binary main likhenge jo hai ‘110001’ jaisa image main diya hua hai.
◼ Ab hum minus(-) sign ko ‘1’ lekhenge or 49 ka ‘110001’ hai lekin hum dekh rahe hai 49 or minus ko mila kar kevel 7 bits hua hai 8 bits main karne ke liye sign bit ke baad or ‘110001’ ke pehle ek zero laga denge jaisa image main kiya hai.
◼ - 49 ko humne boxes main Represent kiya hai toh phela bit joh hai woh signed bit hai jo minus hai or others bits 49 number hai jaisa image main diya hua hai.
◼ - 49 Negative number hai kyoki minus sign hai to isko Signed Integer main Represent karne ke liye ab isko hum Signed 1’s Complement main karnge fir Signed 2’s Complement main karnge.

Signed 1’s Complement :-

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◼ - 49 ke Signed Magnitude ko Signed 1’s Complement main convert karne ke liye Sign bit ko same likh kar baki sabhi bachi hui bits ko change kar denge; ‘1’ ko ‘0’ or ‘0’ ko ‘1’ kar denge jaisa image main kiya hai.
◼ Ab humara Signed 1’s Complement nikal gaya ab hum iska Signed 2’s Complement nikalenge.

Signed 2’s Complement :-

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◼ Signed 2’s Complement main convert karne ke liye jo Signed 1’s Complement aaya hai usme 1 add kar denge jaisa image main diya hai.
◼ Finally humne – 49 ka Signed Integer main Represent kar diya hai.

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