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# negation operator

tue march
Greenhorn
Posts: 16
Hi guys,

public class Flip{
public static void main(String argv[]){
System.out.println(~4);
}
}

can anybody explain why the output of this program is -5.

Good guy

David Harkness
Ranch Hand
Posts: 1646
~ is not negation; it's called two's complement. You flip all the bits, sobecomesCan you see how it can be used for negation?

Ernest Friedman-Hill
author and iconoclast
Marshal
Posts: 24212
35
Originally posted by David Harkness:
~ is not negation; it's called two's complement.

<nerd>
Two's complement would be flipping the bits and then adding one. Just flipping the bits is "one's complement".
</nerd>

Ryan McGuire
Ranch Hand
Posts: 1085
4
To combine and extend what David and Ernest said...

If we just look at 16 bits 4 = 0000000000000100. The ~ does a one's complement operation, so ~4 = 1111111111111011. The - does a two's complement operation, which is the one's complement plus 1, so -4 = 1111111111111100. Since 5 = 0000000000000101, -5 = 1111111111111011, which is the same things as ~4.

Why use two's complement for negative numbers? Because it makes subtraction work. For instance let's try 5 + (-4): 0000000000000101 + 1111111111111100 = 0000000000000001 with a 1 bit that got carried off the left end. With the one's complement, the answer is off by one.

One other clever thing about two's complment is that -0 = 0, while ~0 != 0.

Ryan
[ April 26, 2005: Message edited by: Ryan McGuire ]

David Harkness
Ranch Hand
Posts: 1646
Too long outside of the classroom. Thanks guys for clarifying!