Negative numbers are represented as two's complement. To calculate the negate of the number, in bits, you first complement it (reverse all the bits) and then add 1.
So -1 --> 1111 1111 1111 1111 1111 1111 1111 1111
Another way to think about it is... if you add one to negative one
you should get zero. If you add one to the number above, it should roll over to zero.
Henry