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

1. $ABE$
2. $DBC$
3. $DE5$
4. $9E7$
edited | 3.5k views

539 = 512 + 16 + 8 + 2 + 1 = 29 + 24 + 23 + 21 + 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
Correct Answer: $C$
edited
+1
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.
+3
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

(-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 vote

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