计算机如何添加负数？

Question

So in twos complement, -1 is represented as 11111111 as an 8-bit number.

so how does

11111111
11111111+
_________
11111110

Answer 1

The same as adding positive numbers!

1 + 1 = 10, right? So the true addition is:

  11111111
  11111111+
 _________
 111111110

but we're using fixed-length 8-bit arithmetic, so the leftmost bit is lost, giving the answer

  11111110

or -2.

Another way to look at this is that
bit 0 has value 1
bit 1 has value 2
bit 2 has value 4
..
bit 6 has value 64
bit 7 has value -128 (this is 'the sign bit')

Answer 2

You'd add it just like you would any other value. The addition of the two, least significant bits result in overflow, and the bit is carried over to be added to the second, least significant bit, and so on. Once the two, most significant bits are added, the bit that is carried over (due to overflow) is simply discarded.