Full Adder Circuit – The way it Works

A Full Adder is a digital circuit that performs the addition of three binary inputs. On this tutorial, you’ll learn the way this circuit works, its reality desk, and the best way to implement one utilizing logic gates.

Schematic for a Full Adder Circuit
A Full Adder Circuit

What’s a Full Adder?

Adders can both be Half Adders or Full Adders. The distinction is that the Half Adder is used so as to add solely two 1-bit binary numbers, due to this fact its sum can solely vary from 0 to 2. To enhance this efficiency, the Full Adder was developed. It is ready to add three 1-bit binary numbers, reaching a sum vary from 0 to three, which may be expressed with two output bits (“11”). 

A B Cin S Cout
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1
Full Adder Fact Desk

If you happen to observe the above reality desk, A and B symbolize the enter variables you need to add, whereas  Cin is a carry enter. S is the sum output and Cout is an output to point if a carry has occurred. However in binary logic, what does a Carry imply? Properly let’s see the subsequent instance:

2-bit calculation example

Observe that once you add “0” and “0” or “1” and “0” the outcome may be expressed with only one bit, however once you add “1” and “1” you want two bits, and one in every of them is the carry.

However why do you want a carry enter in full adders? Properly, once you need to sum inputs with greater than 1-bit numbers, for instance including two 4-bit binary numbers, you will have to mix a number of adders and supply a carry enter between them to specific that the earlier much less important operation produced a carry.

The Full Adder Circuit

Full Adder block diagram

A Full Adder may be constructed utilizing two Half Adders circuits and an OR gate. The primary Half Adder has two 1-bit binary inputs, that are A and B. It produces two outputs; Sum and Carry.

The Sum output of the primary Half Adder would be the first enter of the second Half Adder. And the Carry output of the primary Half Adder would be the second enter to the extra OR gate.

The second enter of the second Half Adder turns into the Carry enter (Cin) of the Full Adder.

The second Half Adder may also present Sum and Carry outputs. Its Sum output represents the Sum output (S) of the Full Adder, and its Carry output is the primary enter of the extra OR gate. Lastly, the OR gate will generate the Carry output (Cout) of the Full Adder.

Let’s change the blocks with the precise circuits:

Full Adder Circuit parts

Purposes of the Full Adder: 4-bit Binary Adder

Let’s suppose you need to add the next two 4-bit binary numbers A and B:

A = 1111 B = 1111

The outcome might be a 5-bit quantity:


The place essentially the most important bit signifies a carry.

So so as to add two 4-bit binary numbers as above, you will have to mix 4 Full Adders as follows:

4 bit Binary Adder

As you’ll be able to see, the inputs A and B of every adder comprise the weather of the 2 4-bit binary numbers, distributed from their much less important bits from proper to left. Additionally, observe how the carry output of 1 Full Adder is the carry enter of the subsequent one. Simply keep in mind that is to have in mind if the earlier much less important operation produced a carry.

Try the CMOS CD4008 chip that may add two 4-bit binary numbers.


Do you’ve got any questions in regards to the Full Adder? Let me know within the feedback beneath.

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