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Negative Binary representation

 
Greenhorn
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I just came across this question on a mock exam:
What will be the result if you attempt to compile and run the following code ?
public class Flip{
public static void main(String argv[]){
System.out.println(~4);
}
}
The answer is -5.
I understand that the binary representation of 4 is:
0000 0000 0000 0000 0000 0000 0000 0100
and that after the flip of all the bits, the binary result is:
1111 1111 1111 1111 1111 1111 1111 1011
I know that a 1 in the leftmost position means the number is negative, but I don't understand how th above represents -5.
I realize this is kind of a basic question, but can anyone explain? Thanks.
 
Ranch Hand
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Negative values are stored using 2's complement. To convert a 2's complement value to get its value, you first flip all of the bits and then add 1. In your example, you'd do this:

0101, is, of course, 5. So, whenever you see that you have a binary number (you can tell if the sign bit is a 1), you need to flip the bits and add 1 to determine what that number really is.
If you're still confused or want some extra practice, search for 2's complement on this forum - I'm sure you'll get a lot of results.
I hope that helps,
Corey
 
Theresa Fitzgerald
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Thanks! That makes sense I just haven't seen it explained before anywhere.
 
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Hi Theresa,
If you want to find the complement (~) for any number, you can also use the following expression,
~x=-x-1
Lets say you wanna find complement of 4 that is ~4, we get
 
Abdulla Mamuwala
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Hi Theresa,
If you want to find the complement (~) for any number, you can also use the following expression,
~x=-x-1
Lets say you wanna find complement of 4 that is ~4, we get
~4=-4-1 = -5
I thought this was a nice trick, for the test, instead of flipping bits n all that stuff, but it doesnt hurt to know the fundas.
I hope it helps.
 
Theresa Fitzgerald
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Wow! That will really help out with the exam, plus knowing the fundamentals behind it is a plus. Glad to be part of this group1
 
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