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4 Answers

Best answer
52 votes
52 votes
$539 = 512 + 16 + 8 + 2 + 1 = 2^9 + 2^4 + 2^3 + 2^1 + 2^0$
 $= (1000011011)_2$

Now all answers have 12 bits, so we add two 0's at beginning $= (001000011011)_2$

To convert to 2's complement invert all bits till the rightmost 1, which will be $(110111100101)_2$

$= (1101 1110 0101)_2$
$= (DE5)_{16}$
Correct Answer: $C$
edited by
5 votes
5 votes

(-539)10

Decimal Number which is equivalent to -539 in 2's Complement will be

=N+ 2n 

where N is Given Number and n is range of 2's complement (-2n-1 to 2n-1 -1) in this case to cover -539 in range we have to take n=11 (-1024 to 1023).

so,

=-539+211

= -539+2048

=1509

=(10111100101)2

= 1101  1110   0101 (add 1 as MSB to group in 4 bits for Hexadecimal, here we need to take 1 as number is negative.)

=(D E 5)16

1 votes
1 votes
  1. Convert the absolute value of the decimal number to binary:

    • $539$ (decimal) $=$ $10000101111 $(binary)
  2. Invert all the bits (take the 1's complement):

    • $10000101111$ (binary) -> $01111010000$ (1's complement)
  3. Add 1 to the 1's complement to get the 2's complement:

    • $01111010000 + 1 = 01111010001$ (2's complement)
  4. Convert the 2's complement binary to hexadecimal:

    • $01111010001$ (binary) $=$ $DE5$ (hexadecimal)

Therefore, $DE5$ is the correct 2's complement representation of $(−539)_{10}$ in hexadecimal.

Answer:

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