Electronics and Communication Engineering - Digital Electronics - Discussion


4 bit 2's complement representation of a decimal number is 1000. The number is

[A]. + 8
[B]. 0
[C]. - 7
[D]. - 8

Answer: Option D


(a) and (d) both are option, But there is meaning to represent a positive number in 2's complement form, we take complement representation for negative number only. Therefore most appropriate number is "-8".

Veeresh said: (Nov 26, 2016)  
How it is? Please explain the solutions.

Tharun said: (Feb 3, 2017)  
Negative number representation in 2' s complement is
-8 = 1000.

Then apply 1's complement i.e 0111.
Then add 1to the result i.e 1000.

Dharwendra Pandit said: (Mar 22, 2017)  
1000= 1st term is 1 so negative sign and 2^3 = 8 so -8.

Badhshah said: (Jan 12, 2018)  
The "-" sign depends on the MSB position.

So, the MSB is 1, the answer of 1000 is '-8'.

Bhagyashree said: (Aug 26, 2018)  
In the unsigned binary number MSB bit does not indicate any sign, but in signed binary number MSB indicates the sign.

In sign binary number, If MSB is '1' it indicates the -ve number and '0' indicate the +ve number.


But in 2's complement, MSB has indicated both signs as well as value.
Eg:1000---->-8 (MSB bit is '1'so it is indicated -ve number, '1000'indicates 8 in decimal).

Murali said: (Aug 28, 2020)  
The answer is -7.

Because they ask the number -7 is equal to 0111 and 2's complement of 0111 is 1000.

So answer is -7.

Hagamuchi said: (Aug 23, 2021)  

Do the 2's complement you will get 8.

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