Half Adder

Half Adder :
A combinational circuit that performs the addition of two bits is called half adder. It needs two input bits that are to be added and produces two output bits that are sum and carry.
The truth table for half adder is:

 x y C S
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0

Tips:- Here carry output is 0 unless both input bits are 1.
We can derive simplified boolean function for half adder with the above truth table as :
S = x'y+xy' = x⊕y
C = xy
The half adder can be implemented with an exclusive-OR gate and an AND gate.The logic diagram for this implementation is as below:

   

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