Hi friends, in this video we will be talking
about the adder circuit. If you have been following our channel you would remember that we have covered a video which walks you through addition of binary numbers. Typically, addition of binary numbers gives us the sum term and the carry If in case you need to revise your concepts of adding binary numbers, the link is provided in the description below. But don’t you worry, this video will be sufficient to get the drift of the concept.
So, getting back to this video, adders are basic building blocks of any digital electronics device. You can use them to make your own calculator. Adder circuits make arithmetic
and logical circuits called ALU to compute the binary addition operation on bits of data. Adders are of different types starting from half adders, full adders and ripple carry
adders. lets understand half adder. The half-adder circuit is useful when you want to add one
bit of numbers. We all know by now, one bit takes two values, 0 or 1. Let us refer to the classic truth table we all use when two variables A and B are of one bit each. Here sum indicates the value obtained upon addition and carry indicates whether there has been a carry or not by adding the two numbers. Lets add them. 0 plus 0 is 0 with of course no carry. 0 plus 1 is 1 with no carry. 1 plus 0 is 1 again with no carry. However, one plus one as we know in binary systems, the sum is 0 and there is a carry of one. Also, there is one more
trick to find this. If the number of terms to add, contain odd number of ones, the sum is 1. And for even number of ones, the sum is 0 and carry is 1. Now, I want you all to
analyse the truth table for sum. We see that when variables A and B are both 0 or 1, sum is 0 and when A is 0 and b is 1 or for A is 1 and B zero, the output is 1. This is the
truth table for the XOR gate. Lets present this equation using the xor gate. Let’s
take A and B and connect an XOR gate. The output is the sum term A xor B. Now analyse the truth table for just the carry section. If you all remember the video on basic gates, this is the truth table for AND gate. Lets represent it using an AND gate and that’s
our carry expression. Another way, we can find the boolean expression is by Kmap. Let’s, represent this column which is for carry using it. We will take a 2 input KMAP, the inputs
being A and B. Lets update it, group it and write the boolean expression. Here 1 is present for A and B. The expression for carry is A AND B.Lets update kmap for sum, lets group the terms. Well, no grouping here. And write the expression for this term. This is A AND B bar since, A is 1 and B is 0 so while writing the SOP or sum of products we represent it as A AND B bar. This term here is A bar AND B. We will take both terms and sum them thus writing the sum of the products expression. A AND B bar or A bar AND B is nothing but A xor B and that’s our sum
expression. And if you notice the kmap for sum, its quite peculiar. It represents a check board configuration. Here no grouping is possible since the ones are presented in the check board style. If you see a kmap like this, simply XOR the terms, in this case it is A XOR B. You can write the boolean expression for this and solve it and derive to the same answer. A half adder is built using just two gates, an AND gate to give us the carry term and
XOR gate to give the sum term. One more thing to remember is that the half adder does not take carry from previous sum. The answer to this being that the variables are just one
bit. Hope you have understood the half adder circuit. In the next video, we will talk about full adders.