Tuesday, August 16, 2011

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.

8 comments:

  1. thanks dude..
    it is very helpful for my project :)

    ReplyDelete
  2. this information is much helpful thanks a lot . :)

    ReplyDelete
  3. This is what I have been searching in many websites and I finally found it here. Amazing article. I am so impressed. Could never think of such a thing is possible with it...I think you have a great knowledge especially while dealings with such subjects.

    ReplyDelete
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  6. great for my exam tomorrow ! thamk u :)

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  7. :( this doesn't help me to divide numbers

    ReplyDelete