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12. Binary Multiplication

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Computer Organization & Architecture

1.Binary Subtraction

◼ Binary Subtraction ka ek point rhe gaya tha iske betane k baad main BINARY MULTIPLICATION isi notes main btaunga.
◼ Let's take an example
    (100010)2 - (011101)2 = (?)2
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◼ Phele jha se start from here likha hai wha se subtract krna start karnge.
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◼ Humne ye kiya isme ki 0 ne dekha ki uske pass 1 se subtract hone ke liye kum number hai toh usne apne bagal wale number se borrow liya to 0 ban gya 1 0 (one zero) and 1 kat ke ban gya 0 to agar 1 0 (one zero) ko subtract karnge 1 se to ayega 1 kyoki (1 0)2 = (2)10 hota hai or jab 2 me se 1 minus karnge to 1 milega or 1 ka binary 1 hi hota h jaise image main likha hai.
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◼ Ab dekh rhe h ki agar 0 – 0 = 0 ayega jaisa image main kiya hai.
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◼ Ab hum dekh rhe hai ki 0 chota hai 1 se toh subtract krne k liye apne bagal wale number se borrow lega lekin dekh rhe h ki jab 0 apne bagal wale number se ek number mangega to wo bhi 0 hi h matlab uske pass bhi number ni hai 0 ko dene k liye jaise image main kiya hai.
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◼ Ab kya hoga jab us 0 k pass bhi ni h number dene k liye toh wo kya karga woh 0 apne bagal wale number se borrow mangega lekin hum phir dekh rhe hai ki us 0 ke pass bhi number ni hai dene k liye toh ab kya karga wo aapne aage wale number se mangega jaisa image m dikhaya h.
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◼ Phr woh 0 apne bagal wale number se borrow mangega toh dakh rhe hai ki usko borrow mil jayega kuki uske bagal wale number k pass number hai borrow dene ke liye jaisa image main likha hai.
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◼ Jaisa image m diya hai ki kaise kaise 0 ne borrow liya hai or aage pass kiya h phir humne dekha ki (1 0)2 = (2)10 hota hai toh agar 2 main se 1 minus krnge toh 1 hoga jaise image main kiya hai.
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◼ Ab hum dekh rahe h ki 0 ne borrow liya to bana tha 1 0 lekin fir usne aage pass kar diya tha to 1 0 se kat kar bana 1 or jab 1 m se 1 minus karte h to 0 aayega wahi kiya h. 1 - 1 = 0
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◼ Yaha bhi same wahi ho rha h jo upar wale step m hua.
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◼ Toh ab hum dekh rhe h ki jo 1 sabse pehle likha tha usne to borrow de diya tha to wo 1 kat kar 0 bacha tha or 0 - 0 = 0.
◼ Finally humara answer aagya toh hum aise likhnge.
    (100010)2 - (011101)2 = (000101)2

2.Binary Multiplication

◼ Multiplication toh sab jantey hai kya hota hai jaise humne pedha h.
◼ Example : 56 * 4 = ?
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◼ 56 * 4 = 224 hota hai
◼ Agar ek or example le toh 56 * 14 = ?
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◼ 56 * 14 = 784 hota hai
◼ Lekin ye to decimal number main multiplication hai hume karna hai BINARY MULTIPLICATION .
◼ NOTE:- Binary number m multiplication karte hua sirf 0 or 1 ko hi lenge.
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◼ Toh ab bat kartey hai BINARY MULTIPLICATION ki table main dekh rhe h ki DECIMAL and BINARY multiplication main same same result hota h jaisa ki table main hum dekh sakte hai.
◼ Let's take an example
    (1001)2 * (11)2 = (?)2
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◼ Jha se start from here likha hai wha se multiply karna start karnge jaise image main likha hai.
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◼ Phele 1 se 1 ko multiply karnge 1 * 1 = 1 jaise image main kiya h.
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◼ Phir 1 ko 0 se multiply karnge 1 * 0 = 0 jaise image main kiya hai.
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◼ Phir 1 ko 0 se multiply karnge 1 * 0 = 0 jaise image main kiya hai.
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◼ Phir 1 se 1 ko multiply karnge 1 * 1 = 1 jaise image main kiya hai.
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◼ Ab bari hai next 1 ki ab usko multiply karnge toh jab niche likhnge multiply karke toh phele cross ka sign legaynge jaise image main kiya hai phir muiltiply karke result likhenge jaise image main kiya hai.
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◼ Phir 1 ko 0 se multiply karnge 1 * 0 = 0 jaise image main kiya hai.
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◼ Phir 1 ko 0 se multiply krnge 1 * 0 = 0 jaise image main kiya hai.
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◼ Phir 1 ko 1 se multiply karnge 1 * 1 = 1 jaise image main kiya hai.
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◼ Jaise hi multiply ho jayega toh hum, phir usko add karnge toh jaise image main kiya hai toh humara result aa jayega.
◼ Finally result aa gaya toh hum isko aise likhnge.
    (1001)2 * (11)2 = (11011)2

◼ NOTE:- IMPORTANT EK EASY TRICK HAI DEKH LO EK BAR.


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◼ Jaise ki dekh rhe h ki agar niche likha hua number jo ki circle m likha h wo 1 h to upar likha hua sari ki sari bits same likh denge or agar circle m 0 h to upar jitni bits h jaise ki yaha par 4 bits h to utni hi zero’s matlab ki 4 zero’s likh denge.
◼ Or fir finally addition karke result likh denge.
◼ To ye jo trick h bohot easy h or simple bhi.

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