~ operator in C

Question

The output of this program is -13. I have never fully understood ~ operator in C. Why does it give -13 as output? How to limit ~ operator to just 4 bits of a number?

<         


        

Answer 1

The operator ~ is the logical not in C, i.e. when applied to a integer it flips every single it of its binary representation. Note that defining a integer in simply as int makes it unsigned integer. That means that the first it is used as a sign bit. Since negatives are defines as -a = ~a + 1 you can see that ~a = -a - 1. If you want to flip only the last 4(or more generally the last k) bit of a int you could do something like this

int k = 4;
int mask = (1 << k) - 1;
int b = a ^ mask;

Answer 2

The ~ operator acts as a binary NOT, that is, it flips all the bits in the number. Negative numbers in signed integers are stored as two's complement.

Answer 3

(12)10 in binary is (1100)2

The tilde is the bitwise complement operator which makes 1100 --> 0011. However if you working on a 32 bit platform actually what we get is:

0000 0000 0000 0000 0000 0000 0000 1100

Whose bitwise complement is:

1111 1111 1111 1111 1111 1111 1111 0011
|

Now since the left most bit is for sign the number becomes negative. If you use unsigned int you will be able to understand better what is happening:

unsigned int a = 12;
a = ~a;

Will give:

1111 1111 1111 1111 1111 1111 1111 0011

Which is 4294967283

Answer 4

it's a bitwise operator (one's complement ) that works this way :

~00000101 // 5
=11111010 // 250

so the 1s become 0s and vise versa but in some cases the sign bit is activated and you'll get unexpected results

Answer 5

To limit the effect to a specified number of bits, just use bitwise masks, e.g.:

#include <stdio.h>

int main(void) {
    int a = 16;             /* 10000 in binary */
    int b = ~a;             /* Will interpret b as -17 in two's complement */
    int c = (a & ~0xF) | (~a & 0xF); /* Will limit operator to rightmost 4 bits,
                                        so 00000 becomes 01111, and c will become
                                        11111, not 11...101111, so c will be 31     */

    printf("a is %d, b is %d, c is %d\n", a, b, c);
    return 0;
}

Outputs:

paul@local:~/src/c/scratch$ ./comp
a is 16, b is -17, c is 31
paul@local:~/src/c/scratch$