Find these notes at:
http://public.gettysburg.edu/~cpresser/CS103/

Binary addition
0 + 0 = 00
0 + 1 = 01
1 + 0 = 01
1 + 1 = 10

Input  Output
A  B   Carry Sum
0  0    0     0
0  1    0     1
1  0    0     1
1  1    1     0
       AND   Exclusive OR (XOR)
 
 Adding multidigit numbers
  111   <-carry
  0011
 +0111
 =1010
 
 Add three bits: A, B, Carry In (Cin)
 
 Inputs     Outputs
 A  B Cin    Cout S   ->Carry out (Cout)
 0  0  0      0   0
 0  0  1      0   1
 0  1  0      0   1
 0  1  1      1   0
 1  0  0      0   1
 1  0  1      1   0
 1  1  0      1   0
 1  1  1      1   1
 
 
 Ripple-Carry Adder
 
   A1 A0  e.g.     1 1
  +B1 B0          +1 0
=C S1 S0         1 0 1