NOR gate

A B   A NOR B
0 0       1   <- (NOT A) AND (NOT B)
0 1       0
1 0       0
1 1       0

A NOR B = NOT (A OR B)

Half-adder (add two bits together)

A, B compute A + B in binary


A   B   CARRY  SUM
0 + 0 =   0     0
0 + 1 =   0     1
1 + 0 =   0     1
1 + 1 =   1     0

CARRY = A AND B
SUM = A XOR B

   111
   0101
 + 0011
   1000
   
 Full adder handles one column
 
A B C   Carry Sum
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