In 16-bit 2’s complement representation, the decimal number -28 is:

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GATE CS 2019 Official Paper
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  1. 1111 1111 0001 1100
  2. 0000 0000 1110 0100
  3. 1111 1111 1110 0100
  4. 1000 0000 1110 0100

Answer (Detailed Solution Below)

Option 3 : 1111 1111 1110 0100
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2

28

 

2

14

0

2

7

0

2

3

1

2

1

1

 

0

1

 

2810 = (11100)2 = (0000 0000 0001 1100)2

-2810 = 2’s complement of 0000 0000 0001 1100

2’s complement of 0000 0000 0001 1100 = 1111 1111 1110 0100

Note:

Tricks to find: 2’s complement

Start reading the bits from LSB (right hand side) and write it unless first 1 is encounter, leave the first 1 as it is and complement the remaining bits.
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