Question

$2’s$ complements representation of the following decimal number $-(105.75)_{10}$ is:

• A. $10010110.01$
• B. $10011110.01$
• C. $10001110.10$
• D. $11001011.10$

 

Comments

(A) is the answer bro.

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when we take 2's complement.....do we consider decimal part together with whole & then aplly 2's complenet method ?

Answer 1

Method 1: $\color{blue}{-(105.75)  = -106 + 0.25}$

Convert both of these to $2's$ complement representation and add them.

$10010110 = -128 + 16 + 6 = -106 $ and $0.25 = 0.01$ So, combining these two, we get $\color{red}{-(105.75) = 10010110.01}$

Method 2:  This is the method we generally follow to find $2's$ complement representation of any negative number.

• Firstly find binary representation of $+ve$ number i.e., $(105.75)_{10} =  01101001.11$
• Take $1's$ complement of the number, now we get $10010110.00$
• Now, add $1$ to LSB, So we add $0.01$ here to above number.
• $10010110.00 + 0.01 =  10010110.01 $

PS:) I followed method $1$, when I gave this test.

Answer 2

105.75 in binary is written as  01101001.11

now apply 2's complement u will get the answer as A)