Prove that the circuit in the notes is a full adder:
abciab a xor b (a xor b) xor ci (a xor b) ci ((a xor b) ci) + ab sc0
0 0 0 0 0 00 000
0 0 1 0 0 10 010
0 1 0 0 1 10 010
0 1 1 0 1 01 101
1 0 0 0 1 10 010
1 0 1 0 1 01 101
1 1 0 1 0 00 101
1 1 1 1 0 10 111
Note the (a xor b) xor ci and s match

Note (a xor b) ci + ab and co match