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Question

The decimal equivalent of given 2’s complement number $(110101011.1101)_2$ is:

Comments

Ans: $- 84.1875$  ?

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Don't just copy paste their answer give some logic atleast so others can verify it

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$(110101011.1101)$ is in $2’s$ compliment representation. MSB is $1$ so we we know it is a negative number.

Do $2’s$ complement of given singed binary number is $(001010100.0011)$.

Converting it to decimal $64+16+4+ \frac{1}{8} +\frac{1}{16} = 84.1875$.

So final answer is $-84.1875$

Answer 1

The given number is  110101011.1101. Separate the number from decimal point

It separates as  110101011 and 1101.

 110101011 is in 2’s complement and it’s MSB is 1 so it is negative number. In order to find it’s magnitude we have to find 2’s complement of it . 

2’s complement of  110101011 is   001010101  and its decimal equivalent is 85 . So magnitude is  -85

To find value after the decimal point just multiply each term by negaive power of 2.

 

So 1101 = 1*2^-1  + 1*2^-2  + 0 + 1*2^-4 

It becomes  0.8125

 

So overall ans will be    -85.8125

Comments

@dadu just a small correction that in decimal part, the last term will have -4 as the power. -3 is absent due to 0 in binary form.

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Yeah , very true , that was typo, thanks for noticing it.

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why are you subtracting 0.8125 from -85?

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-85.8125 is the wrong answer.

Using the weighted property of 2's complement we have

-256 + 128 + 32 + 8 + 2 + 1 + 0.5 + 0.25 + 0.0625 = -84.1875

Even if we calculate the 2's complement of the given binary number we get

(001010100.0011)₂ = 64 + 16 + 4 + 0.125 + 0.0625 = 84.1875 this is the magnitude of the number and the number will be negative as we have taken the 2's complement, hence -84.1875

for reference use this link

https://stackoverflow.com/questions/15463491/how-to-represent-a-negative-number-with-a-fraction-in-2s-complement