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+16 votes
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The $2's$ complement representation of the decimal value $-15$ is

  1. $1111$
  2. $11111$
  3. $111111$
  4. $10001$
asked in Digital Logic by Veteran (59.6k points)
edited by | 1.1k views

4 Answers

+20 votes
Best answer
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.
answered by (399 points)
selected by
+11 votes

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

answered by Boss (45.3k points)
0

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

0 votes
steps:-

1.compliment of the bits  (0000)

2.add one to the result  (0001)

the answer is front of you  (10001)
answered by Active (3.9k points)
0 votes

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.

answered by Active (3.9k points)
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