Half Adder and Full Adder Explained (Digital Logic Part 10)

Welcome to intro to digital logic part 10. In this video we will be going over half adders and full adders.
As a refresher here is the logic ouputs for an exclusive or gate
and an gate
and an or gate
So to begin lets go over half adders. Half adders consists of a and b inputs tied to an exclusive or that outputs a S or sum bit and the a and b inputs also go to a and gate that out puts a carried bit.
So lets go over some binary addition to see how this works.
If we add 0 plus 0 this equals 0 this is the exclusive ore ouput
If we add 1 plus zero or zero plus 1 this equals 1 this is also the exclusive or ouput
If we added one plus 1 this equals zero which is the ouput of the exclusive or and the next bit flips to a 1. The next bit is the carried bit which is and gate carried output.
The flaw of the half adder is that it can only generate a carry ouput and can not take a carry input
The full adder can take a carry bit and the logic gate diagram is listed on this slide for your reference this is hard to look at so lets look at a block diagram.
Really this is 2 half adders combined with an or gate to make a full adder. This is full adder is a half adder with its carry bit hooked into an or gate and the sum bit tied into the a input of another half adder. The second half adder also has b input connected to a carry in bit from a previous operation. This half adder outputs to an or gate with an output of carry out and the an ouput of a sum bit.
Now to explain the binary addition lets first go over normal addition of 7 plus 9.
We would take the 7 plus 9 and get a 6 then we would carry over a 1
This one drops down to give us 16
So now do a binary addition of 2 inputs that values are both 1 bit we get for the first digit the sum of these 2 bits equals zero
The 1 then gets carried over to the second digit addition which carry in plus a plus b equals the sum
This result in binary 1 in second position and 0 in the first position.
Now the full adder is doing the same thing if there is a carry for a previous digit it is added to the a and b input to result in a sum digit and a carry out digit
So an carry in of 0 plus a a in put of 0 plus a b input of zero equals a carry out of zero and a sum of zero
a carry in of 0 plus a a in put of 0 plus a b input of 1 equals a carry out of zero and a sum of 1
a carry in of 1 plus an a in put of 0 plus a b input of 1 equals a carry out of 1 and a sum of 0
a carry in of 1 plus an a in put of 1 plus a b input of 1 equals a carry out of 1 and a sum of 1



Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.