1's complement addition of outer carry to the result
I only understand two's complement

Let's take two 3 bits numbers, X and Y

Complementing the bits is like calculating 111-X

(it is obvious as $\overline {b} = 1-b$, $\sum_{i=0}^n 2^i*(1-b_i) = \sum_{i=0}^n 2^i -  \sum_{i=0}^n 2^i*b_i$...)

The addition becomes 111-X+Y

If you add 1 you get 1000-X+Y. The leftmost carry is discarded.