Complement to 1 and complement to 2

1. Operator -

This operator is simple, you simply get the same value changed sign. If it is positive, it becomes negative; and if it is negative, it becomes positive.

So in your case -a where a=2 the result is -a=-2

2. Operator ~ called bitwise complement

This is more interesting. What this operator does is exchange the representation in binary of the number. That is, let's say the ~2 :

• 2 in binary is: 0000 0010
• we do an exchange of its bits (all 0 to 1 and all 1 to 0 ) the result is: 1111 1101 which is the representation in binary of -3 .
• So ~2 = -3

Let's go to your specific case, which is ~0

• we start from the 0 that in binary is: 0000 0000
• We exchange all the bits: 1111 1111 which is the representation in binary of -1 .
• So ~0 = -1

You have more documentation from the operators here (for java).

To finish simply commenting how they say in this answer from SO original:

The bitwise operator (~) ONLY EXCHANGES BITS. It is up to the machine to interpret them.

Why do I comment on this? To the naked eye the operator ~ is simply to change sign and subtract 1 . That is:

~x = -x - 1

I imagine that there was your question. But it depends on the computer the interpretation of the operator bits ~ is not always the same.

But as it says Paul Vargas in the chat :

  

Since the question is labeled with java there should be no results rare (that there are, for example, in c when work with unsigned - see this link )

    

In the first assignment c = -a; you are using the "minus" symbol to deny the number contained in a so the value of c will be the negative of a : -2. It is the equivalent of multiplying by -1.

In the second case you are using the bit-level denial operator ~ also called "tilde". This operator inverts the 0s and 1s of the number. In this case the number is 0 and its representation in binary is 000000000. When applying the binary negation the resulting binary number is 11111111.

The binary number 11111111 represents the number -1 in decimal given that the representation "complement to 2" is used. To learn more about the add-on to 2 you can read the wikipedia entry

First of all we can start by reviewing what each of the operations is about:

• Supplement to 1

  The complement to 1 of a binary number is obtained by changing 0 → 1 and 1 → 0 . That is, each bit is changed by its complement. For example (using a byte ):

    0 0 0 0 0 0 1 0    Original        ( =  2 )
    ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
    1 1 1 1 1 1 0 1    Complemento a 1 ( = -3 )
  

  See Wikipedia on Complemento a uno .

• Complement to 2

  The complement to 2 of a binary number is obtained by taking the complement to 1 of the number and then adding 1 to the least significant bit ( LSB or Least Significant Bit ). Taking the previous example:

    0 0 0 0 0 0 1 0    Original        ( =  2 )
    ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
    1 1 1 1 1 1 0 1    Complemento a 1 ( = -3 )
  +               1
    ───────────────
    1 1 1 1 1 1 1 0    Complemento a 2 ( = -2 )
  

  The complement to 2 of 0 is 0 ( 00000000 → 11111111 → 00000000 ) and the complement 2 of the most negative number, Byte.MIN_VALUE , is the same ( 10000000 → 01111111 → 10000000 ).

  See Wikipedia on Complemento a dos .

Now, analyzing the code:

• c = -a; // resultado c = -2

  If a = 2 (positive), then c = -a is calculated:

  0000 0000 0000 0000 0000 0000 0000 0010    Original         ( =  2 )
  1111 1111 1111 1111 1111 1111 1111 1101    Complemento a 1  ( = -3 )
  1111 1111 1111 1111 1111 1111 1111 1110    Sumando 1 al LSB ( = -2 )
  

  Or the complement to 2.

  See §15.15.4 within the The Java Language Specification . < br>
  

• c = ~b; // resultado c = -1

  If b = 0 (positive), then c = ~b is calculated:

  0000 0000 0000 0000 0000 0000 0000 0000    Original         ( =  0 )
  1111 1111 1111 1111 1111 1111 1111 1111    Complemento a 1  ( = -1 )
  

  See §15.15.5 within the The Java Language Specification .