Full Adder Video Lecture | Analog and Digital Electronics - Electrical Engineering (EE)

In the previous video, we have discussed about
the half adder circuit.
This video will be about full adder circuit.
If you have missed our previous video you
can find the link for the same in the description
box below.
One of the main drawback of half adder is
its inability to add carry from the previous
addition to the next bits.
This is taken care using the full adder circuit.
The full adder circuit consists of three input
bits and two output bits.
The three inputs 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 outputs are S and Co, where S is the Sum
bit and Co is the carry bit generated for
this sum.
As seen here, let us consider this black box
with 3 inputs as A, B and Ci and 2 outputs
named as S and Co.
The truth table for the full adder is also
shown here.
We can see that the output of 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.
We will try to derive a Boolean equation for
the outputs using K map.
If you have doubt regarding K-map reduction, there is video link in the video
description that might help you.
Let us start by finding out what makes up
the S bit.
On performing reductions using K-map, we find
that S is obtained by ex-oring A, B and Ci.
Similarly let us try for Co bit.
After performing reduction, 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.
We now have a clear understanding of what
is actually inside the black box of full adder.
Let us try implementing the circuit for full
adder.
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 Circuits are available
off the shelf which can be used for your applications.
We hope that you have clearly understood the
working of full adder circuit.