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13. Binary Addition & Subtraction with Fixed or Radix Point

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Computer Organization & Architecture

1. Binary Addition & Subtraction with Fixed/Radix point

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◼ Computer Organization main iss point ko hum FIXED ya fir RADIX point boltey jaise image main diya hai.
◼ Simple addition kaise kartey hai agar radix point laga ho toh.
◼ Jaise 56.4 + 78.9 = ?
◼ Lekin ye Decimal number ka example h.
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◼ Ye simple addition hai joh hum kartey h jab radix point laga hota hai ab bat kartey hai Binary number main Addition ki.
◼ NOTE:- Binary number m Addition ya Subtraction karte hua sirf 0 or 1 ko hi lenge.

2.Binary Addition

◼ Let's take an example
    (111.01)2 + (101.11)2 = (?)2
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◼ Jha se start from here likha hai wha se add karna start karnge .
◼ Ab hum agar 1 + 1 kartey hai toh 2 aata hai lekin 2 toh decimal number hai hume likhna hai Binary main toh 2 ka binary hota hai 1 0 (one zero) toh 0 niche likha hai or 1 upar carry par chala gya hai jaisa image main likha hai.
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◼ Ab hum agar 1 + 0 kartey hai to 1 hota hai lekin 1 carry bhi hai toh carry wala 1 bhi add krnge toh 1 + 0 = 2 hota hai lekin 2 toh decimal number hai hume binary main likhna hai toh 2 ka binary 10(one zero) hota hai , 0 niche likha hai 1 radix point k bad carry main chla gya hai jaisa image main likha hai.
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◼ Ab agar 1 + 1 = 2 hota hai lekin 1 carry bhi toh use bhi add karna hai 2 main toh 2 + 1 = 3 hota hai lekin 3 toh decimal number hai or hum binary main kr rhe toh 3 ka binary 1 1 ( one one) hota hai, 1 niche likha hai or 1 carry main likha hai jaisa image main hai.
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◼ Ab 1 + 0 = 1 or 1 + 1 = 2 or 2 ka binary 1 0 (one zero) , 0 niche 1 carry jaisa image main likha hai.
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◼ Ab 1 + 1 = 2 or 2 + 1 = 3 or 3 ka binary 1 1 (one one) , 1 niche likh denge or dusra 1 carry main nahi niche hi likhnge kyoki aage kuch bhi ni h aad karne ko jaisa image main likha hai.
◼ Finally humara result aagya toh hum aise likh denge.
    (111.01)2 + (101.11)2 = (1101.00)2
◼ Let's take an another example
    (1001.101)2 + (11.01)2 = (?)2
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◼ Jaisa hum dekh rahe h ki pehle wale number (1001.101) m jyada bits h or dusre number (11.01) m kum bits h to kaise karenge.
◼ Sabse pehle dono number likh lenge ek upar or dusra niche lekin Radix point ke exact niche radix point hi lagega.
◼ Fir Radix point ke left m jitni bits h likh denge or right m jitni bits h use bhi likh denge jaisa image m kiya h.
◼ Ab jha se start from here likha hai wha se add kerna start karge lekin ek bat dekhiye ki 1 ke sath add karne ke liye koi number nahi h to waha hum 0 likh lenge or 1 ko 0 ke sath add karnge.
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◼ Ab 1 + 0 = 1 hota hai jaise image main likha hua hai.
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◼ Yaha bhi 0 + 1 = 1 hi hota hai jaise image main lkha hua hai.
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◼ Ab 1 + 0 = 1 hota hai aur radix point k bad wala addition ho gya aur radix point bhi lega diya hai jaisa image main likha hua hai.
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◼ Ab dekh rhe hai ki 1 + 1 = 2 hota hai or 2 binary 1 0 (one zero) hota hai, 0 niche 1 carry jaisa image main likha hai.
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◼ Ab 1 + 0 = 1 or 1 + 1 = 2 or 2 ka binary 1 0 (one zero) , 0 niche 1 carry jaisa image main likha hai.
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◼ Ab 0 + 0 = 0 hota hai or 1 carry bhi hai toh 1 bhi add karnge toh 0 + 1 = 1 hota hai jaisa image main likha hai.
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◼ Ab 1 + 0 = 1 hota hai jaisa image main kiya hai.
◼ Finally humara result aa gaya toh hum isko aise likhnge .
    (1001.101)2 + (11.01)2 = (1100.111)2

2.Binary Subtraction

◼ Hum sabse pehle simple subtraction ki bat kartey h.
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◼ Hum dekh rhe hai ki yha par radix point main subtract kaise kartey hai lekin ye decimal subtraction hai or hume karna hai binary subtraction toh start krtey hai BINARY SUBTRACTION.
◼ Let's take an example
    (111.01)2 - (11.10)2 = (?)2
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◼ Jha se start from here likha hai wha se subtract karna start karnge.
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◼ Ab hum dakh rhe hai ki 1 – 0 = 1 hota hai jaisa image main likha hai.
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◼ Ab dekha ki 0 joh hai woh small hai toh 1 se minus ni ho payega phele woh apne bagal wale number yani 1 se borrow lega to 1 borrow de dega to wo 1 kat kar 0 ban jayga or jo 0 borrow le ra h woh banega 1 0(one zero) or (1 0)2 = (2)10 hota hai 2 – 1 = 1 hota hai.
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◼ Ab dekh rhe hai ki ye bit phele 1 tha isne apne right wale bit ko borrow diya toh ye ho kat kar 0 ban gaya tha ab ye bhi apne left side wale number se borrow lega toh banega 1 0(one zero), ab 1 0 = 2 hota hai or 2 – 1 = 1 hota hai 1 0 ka matlab 2 hota hai.
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◼ Ab dekh rhe hai ki ye wala bit bhi phele 1 tha isne bhi apne right wale bite ko borrow diya tha toh ye bhi 0 ho gaya tha ye bhi apne left wale number se borrow lega toh banega 1 0(one zero) , ab (1 0)2 = (2)10 or 2 - 1 = 1.
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◼ Ye bhi phele 1 tha isne apne right wale bit ko borrow diya toh 0 ho gaya tha or ab 0 m se minus karne ke liya koi bhi bit nahi bachi to hum 0 ko hi niche likh denge.
◼ Finally humara result aa gaya toh ab hum isko aise likha denge.
    (111.01)2 - (11.10)2 = (011.11)2
◼ Let's take an another example
    (1101.01)2 - (10.010)2 = (?)2
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◼ Jha se start from here likha hai wha se subtract karna start karnge jaisa image main diya hai.
◼ Ab hum dekh rahe h ki 0 ke upar koi number nahi h minus karne ke liye to jaha par bhi koi bit nahi hoti waha hum 0 laga lete h.
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◼ Ab 0 – 0 = 0 hota hai jaisa image main likha hai.
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◼ Ab 1 – 1 = 0 hota hai jaisa image main likha hai.
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◼ Ab 0 – 0 = 0 hota hai jaisa image main likha hai.
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◼ Ab 1 – 0 = 1 hota hai jaisa image main likha hai.
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◼ Ab dekh rhe hai ki 0 small hai toh woh apne left wale number se borrow lega toh woh banega 1 0 (one zero) toh (1 0)2 = (2)10 hota hai agar 2 - 1 = 1 hota hai kyoki 2 ka matlab 1 0 hota hai waise hi 1 0 – 1 = 1 hoga jaisa image main likha hai.
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◼ Ab hum dekh rhe hai ki phele ye wala bit 1 tha toh jb isne apne right wale bit ko borrow diya tha to 1 kat kar bacha 0 or ab ye borrow to nahi lega kyoki niche bhi 0 hi h toh ab 0 – 0 = 0 hota hai jaisa image main likha hai.
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◼ Ab 1 – 0 = 1 hota hai jaisa image main likha hai.
◼ Finally humara result aa gaya toh hum isko aise likhnge.
    (1101.01)2 - (10.010)2 = (1011.000)2

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