ADDERS:
Lets design the combinatonal 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 Kmap also which are discussed on the next page
Kmap for the variable Sum is
Kmap for the variable Carry is
And the circuit diagram is as follow:
