Full Adder Circuit

A Full Adder is a combinational circuit that performs the arithmetic sum of three input bits. It consists of three inputs and two outputs. Three of the input variables can be defined as A, B, Cin and the two output variables can be defined as S, Cout. The two input variables that we defined earlier A and B represents the two significant bits to be added. The third input Cin represents the carry bit. We have to use two digits because the arithmetic sum of the three binary digits needs two digits. The two outputs represents S for sum and Cout for carry.

For designing a full adder circuit, two half adder circuits and an OR gate is required. It is the simplest way to design a full adder circuit. For this two XOR gates, two AND gates, one OR gate is required. 

Truth Table   

 

Input A	Input B	Input Cin	Output Cout	Output S
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

Solution using K-map

For S

A\BCin 00          01             11            10        

	1		1
1		1

 S=A'B'Cin+A'BCin'+AB'Cin'+ABCin

For Cout

A\BCin  00                      01                           11                         10

		1
	1	1	1

 Cout=AB+ACin+BCin

Circuit Diagram

Implementation Using Boolean Function

For S

S=Cin XOR (A XOR B)

 =Cin'(AB'+A'B)+Cin (AB'+A'B)'

 =Cin'(AB'+A'B)+Cin(AB+A'B')

 =AB'Cin'+A'BCin'+ABCin+A'B'Cin

For Cout

Cout=Cin(AB'+A'B)+AB

   =AB'Cin+A'BCin+AB

This is the simple design procedure of Full Adder circuit.