In this tutorial we are going to learn about on Full adder circuit.

Full Adder β
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 βor 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.

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