Question

When I complement 1 (~1), I get the output as -2. How is this done internally?

I first assumed that the bits are inverted, so 0001 becomes 1110 and then 1 is added to it, so it becomes 1111 which is stored, how is the number then retrieved?

Answer 1

Well, no. When you complement 1, you go just invert the bits:

 1  ==  0b00000001
~1  ==  0b11111110

And that’s -2 in two’s complement, which is the way your computer internally represents negative numbers. See http://en.wikipedia.org/wiki/Two's_complement but here are some examples:

-1  ==  0b11111111
-2  ==  0b11111110
 ....
-128==  0b10000000
+127==  0b01111111
 ....
+2  ==  0b00000010
+1  ==  0b00000001
 0  ==  0b00000000