Lets design the combinational circuit for binary adder. A combinational circuit that performs the addition of two bits is called Half adder while the circuit which adds 3 bits is called Full adder.
Half adder: For this adder we have two inputs and two outputs. The two inputs are those 2 bits a and b which are to be added and the the 2 outputs are the sum and the carry. The following table shows the result of different combinations of inputs:
a b S(sum) C(carry)
0 0 0 0
1 0 1 0
0 1 1 0
1 1 0 1
Now we can see from the table that carry is one only when both inputs are 1 while sum is 1 when only one of the two is 1 like a XOR gate.So
S= a’b + ab’
C= ab
Or we can get the equations from the K-map also which are discussed on the next page
K-map for the variable Sum is
K-map for the variable Carry is
And the circuit diagram is as follow:
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