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The $2's$ complement representation of the decimal value $-15$ is

1. $1111$
2. $11111$
3. $111111$
4. $10001$

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D) is the correct ans.In 2's complement representation, positive numbers are represented in simple binary form and negative numbers are represented in its 2's complement form. So, for -15, we have to complement its binary value - 01111 and add a 1 to it, which gives 10001. Option D.

Convert the magnitude, -15 to binary.

1111

To make it 8 bits pad 4 extra bits to 1111 (Always Before)

00001111

Negate the number by inverting the bits and adding 1.In simple words

Take the 2's complement of the no

11110001 (from LSB when u see ist 1 leave it as it is and thereafter flip the all bits.)

To match the answer  ignore most significant 3 bits ANS - 10001

### 1 comment

actually 5 bits required to represent -15 in 2's compement

because range of 2's complement no is -2n-1 to +2n-1-1

steps:-

1.compliment of the bits  (0000)

2.add one to the result  (0001)

the answer is front of you  (10001)

For -15, we have to complement its binary value - 01111..

actually 5 bits required to represent -15 in 2's compement

because range of 2's complement no is -2n-1 to +2n-1-1 .. therefore it will be 10001

In 2's complement representation positive integers are represented in its normal binary form while negative numbers are represented in its 2's complement form.

since the given value is negative, the MSB gets a negative weight

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$\therefore option~ \large D$

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