bitwise not operator

Question

Why bitwise operation (~0); prints -1 ? In binary , not 0 should be 1 . why ?

Answer 1

You could imagine the first bit in a signed number to be -(2^{x -1}) where x is the number of bits.

So, given an 8-bit number, the value of each bit (in left to right order) is:

-128 64 32 16 8 4 2 1

Now, in binary, 0 is obviously all 0s:

    -128 64 32 16 8 4 2 1
0      0  0  0  0 0 0 0 0 = 0

And when you do the bitwise not ~ each of these 0s becomes a 1:

     -128 64 32 16 8 4 2 1
~0      1  1  1  1 1 1 1 1
 =   -128+64+32+16+8+4+2+1 == -1

This is also helpful in understanding overflow:

     -128 64 32 16 8 4 2 1
126     0  1  1  1 1 1 1 0  =  126
 +1     0  1  1  1 1 1 1 1  =  127
 +1     1  0  0  0 0 0 0 0  = -128  overflow!