Value of ~10

[Swathi Sree]

Hi All,

I am not able to understand how come ~10 is displaying -11?
the Binary value of 10 is 1010 and one's complement gives 0101 which is 5. As the sign bits are changed, it should be -5. If I print the binary string, then also it is printing "11111111111111111111111111110101".
But if I print toString it is again giving same -11.

Any body please clarify how it is displaying -11.

Thanks in Advance,

Regards,
Swathi.

[Barry Gaunt]

Hint: there are 32 bits in an int. You are only considering 4 of them. What about the other 28 bits?

[Swathi Sree]

Thanks for pointing out that only 4 bits are considered. Even if I consider all bits except the top most bit(sign bit) ita giving 2147483637. resulting in negative sign gives -2147483637.

To get the decimal number of the ones complementation of 10, I used calculator.But in the exam that won't be available(I am preparing for the java certification). Is there any way to calculate this easily?

Thanks & Regards,
Swathi.

[Barry Gaunt]

First a bit of maths: By using 2 complement we get -x = ~x + 1.
So ~x = -x - 1 = -(x + 1). Using that, ~10 = -(10 + 1) = -11.

Now let's try with bits:

 0000 0000 0000 0000 0000 0000 0000 1010  // 10
 1111 1111 1111 1111 1111 1111 1111 0101  // ~10 <- clearly a -ve number, so
                                               // to find what it is
 0000 0000 0000 0000 0000 0000 0000 1010  // flip the bits and
+0000 0000 0000 0000 0000 0000 0000 0001  // add one
=======================================
 0000 0000 0000 0000 0000 0000 0000 1011  // 11 (negative) [B]So ~10 = -11[/B]
 
 

[ August 27, 2005: Message edited by: Barry Gaunt ]

[Rick O'Shay]

What you are missing is that Java uses twos complement.

You took the complement of 10 correctly. I will round off to a byte for clarity:

00001010 -> 11110101

To get the value of a negative number you need to take the twos complement: flip and add one and negate. Try it, it's -11!

11110101 -> 00001010 -> 00001011 -> 11 -> -11

[Ilja Preuss]

With other words, the sign bit doesn't work the way you think it works. Putting a sign bit in front of a binary 5 doesn't make it a -5.

There are at least two reasons to use the two's complement:

- you don't waste the zero (if it worked like you thought, there also would be a negative zero), and

- addition with negative numbers works *exactly* like with positive numbers. That is, if you have four bit numbers

  1110 = -2
+ 0001 =  1
-----------
  1111 = -1