In this tutorial we are going to learn about on Full adder circuit.
Full Adder – The full adder circuit consists of three input bits and two output bits.
The three input to the full adder are A, B and Ci, where A and B are the bits to be added and Ci is the previous carry bit. The output is S and Co, where S is the sum bit and Co is the carry bit generated for this sum. As per below circuit can see here is the 3 inputs as A, B and Ci and 2 outputs as S and Co.
Below is the truth table for full adder:
As can see the truth table that output of the sum is high whenever there are odd number of high inputs and Co bit is high if at least 2 or more than 2 inputs are high.
Here we will try to derive a Boolean equation for the output using K map.
Now we will find out the S, we find that S is obtained by ex-oring A, B and Ci.
Co is obtained as AB + BCi + ACi.
Now since we have the Boolean expressions, we can build the adder circuit using EX-or, OR and AND gates. Now we have the clear understanding of what is actually inside the below circuit.
As seen here the inputs A,B and Ci are connected to 3 input EX –or gate whose output is S bit. AB, BCi and ACi are connected separately to 3 AND gates and the output of these gates is connected to OR gate, whose output corresponds to Co. In this manner one can build a full adder using basic gates. However one does not need to build such a circuit to use full adder. Full adder integrated circuit is available off the shelf which can be used for your applications.