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+20 votes

The $2's$ complement representation of (-539)10 in hexadecimal is

  1. $ABE$
  2. $DBC$
  3. $DE5$
  4. $9E7$
asked in Digital Logic by Veteran (59.9k points)
edited by | 3k views

3 Answers

+28 votes
Best answer

539 = 512 + 16 + 8 + 2 + 1 = 2+ 2+ 2+ 2+ 20
 = (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

answered by Veteran (384k points)
Why we are not concerned about the sign of the given decimal number? If in question +539 base 10 was given, will it not change anything?

Edit: Sorry for very silly question, I got it now, if it would have been positive 539, we would not have done 2's compliment at all.
If +539 will be given then we will only convert it in binary and from binary by appending zero in MSB by making it easy for grouping , using grouping of 4 we will convert it in hexadecimal.  


PS :- 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
+1 vote


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).



= -539+2048



= 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

answered by Active (1.2k points)
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answer - C
answered by Loyal (8.8k points)

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