Code360 powered by Coding Ninjas X Naukri.com. Code360 powered by Coding Ninjas X Naukri.com
Last Updated: Mar 27, 2024
Difficulty: Easy

Difference between Half Adder and Full Adder

Leveraging ChatGPT - GenAI as a Microsoft Data Expert
Speaker
Prerita Agarwal
Data Specialist @
23 Jul, 2024 @ 01:30 PM

Introduction

A half adder adds two single bits, while a full adder can add two single bits along with a carry bit from a previous addition.

Blog Thumbnail

In this article, we will discuss the difference between Half Adder and Full Adder. We will discuss what Half Adder and Full Adder are. The Half and Full Adders are combinational Logical Circuits. They are used to perform various arithmetic functions in the digital circuit. Before moving on to the key difference between them. Let us understand what Half Adder and Full Adder are.

What Is Half Adder?

Half Adder is a combinational logic circuit designed to add two binary bits. It is designed by connecting one AND gate and an EX-OR gate. The Half Adder has two input terminals A and B and two output terminals for sum and carry.

Half Adder

In Half Adder, the output of the AND gate is the carry of the two bits, and the output of the EX-OR gate is the sum of the two bits. Due to the absence of any logic gate, we cannot forward the carry we obtain in one addition into another addition. So, it is called the Half Adder circuit.

Logical Expression of Half Adder

The carry equation is written in the form of AND operation, and the sum equation is in the form of EX-OR operation.

          Sum, S = A ⊕ B

          Carry, C = A . B

    where, ‘⊕’ = XOR

    and        ‘.’  = AND

Truth Table

Input

Output

Terminal A

Terminal B

Carry, C

Sum, S

0

0

0

0

0

1

0

1

1

0

0

1

1

1

1

0

Get the tech career you deserve, faster!
Connect with our expert counsellors to understand how to hack your way to success
User rating 4.7/5
1:1 doubt support
95% placement record
Akash Pal
Senior Software Engineer
326% Hike After Job Bootcamp
Himanshu Gusain
Programmer Analyst
32 LPA After Job Bootcamp
After Job
Bootcamp

What Is Full Adder?

Full Adder is a combinational logic circuit designed to add three binary bits. It is a circuit that has one OR gate, two AND gates, and two EX-OR gates. 

Among all the input circuits, one is for the carry of the bits that we obtained from the previous addition asC-IN. The other two inputs are  A and B.

Full Adder

The carry obtained in the addition process is given to the Full Adder as input, and it adds that carry along with other inputs. Thus, it is named Full Adder combinational logic circuit.

Logical Expression of Full Adder

The output obtained by the  EX-OR gate is the sum of all three binary digits, and the output obtained by the AND gate is the carry of the addition.

          CARRY-OUT = AB + ACin + BCin

          SUM = Cin ⊕ (A ⊕ B)

    where, ‘⊕’ = XOR

Truth Table

Input Output
A B Carry, Cin SUM CARRY-OUT
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

Difference between Half Adder and Full Adder

The key difference between Half Adder and Full Adder are as mentioned below:

Parameter Half Adder Full Adder
Definition Half Adder is a combinational logic circuit designed to add two binary bits. Generates both sum and carry of inputs. Full Adder is a combinational logic circuit designed to add three binary bits. Generates sum of all three inputs with carry value.
Circuit Component The circuit is designed by connecting one AND gate and an EX-OR gate. The circuit consists of one OR gate, two AND gates, and two EX-OR gates.
Carry Bit It does not add the carry obtained from the previous addition to the next. It adds the previous carry along with the current.
Total Inputs Two input terminals - A and B for two bits addition. Three input terminals - A, B, and Cin.
Speed Half Adder is faster than Full Adder as it uses less number of logic gates. Full Adder is slower than Half Adder due to the Carry operation.
Usage It is used in measuring devices, calculators, and Computers/laptops in real-time applications. It is used in Digital Processors, in the addition of multiple bits, and also can be used in place of Half Adder.
Logic Expressions

Sum, S = A ⊕ B

Carry, C = A . B

CARRY-OUT = AB + ACin + BCin

SUM = Cin ⊕ (A ⊕ B)

Must Read Shift Registers in Digital Electronics

Frequently Asked Questions

What are adders and their types?

An adder is a combinational logic circuit used to add binary bits and give the result as an output. There are two types of adders Half Adders and Full Adders.

What is the key difference between Half Adder and Full Adder?

Half Adder is designed to add two binary bits and the circuit consists of one AND gate and an EX-OR gate, whereas Full Adder is designed to add three binary bits and circuit consisting of one OR gate, two AND gates, and two EX-OR gates.

What are the advantages of a Full Adder over a Half Adder?

In the Half Adder, due to the absence of any additional logic gate, we cannot forward the carry you obtain in one addition. Therefore, the Full Adder is designed to take this carry as the third input (Cin) and it adds that carry along with other inputs.

What is the major difference between half adder and full adders quizlet?

Half adder computes sum and carry from 2 bits; full adder computes sum and carry from 3 bits, including a carry input.

What is the difference between a full adder and a parallel adder?

Full adder calculates sum and carry from 3 bits; parallel adder uses multiple full adders for faster arithmetic operations.

Conclusion

This article briefly discussed the difference between Half Adder and Full Adder. We have discussed the Half Adder and Full Adder and what they are used for. You can check out our other blogs to enhance your knowledge:

You can refer to our guided paths on the Coding Ninjas Studio platform. You can check our course to learn more about DSADBMSCompetitive ProgrammingPythonJavaJavaScript, etc. 

We hope this blog helped you to understand the difference between Half Adder and Full Adder. To practice and improve yourself in the interview, you can also check out Top 100 SQL problemsInterview experienceCoding interview questions, and the Ultimate guide path for interviews

Happy Learning!!

Topics covered
1.
Introduction
2.
What Is Half Adder?
2.1.
Logical Expression of Half Adder
2.2.
Truth Table
3.
What Is Full Adder?
3.1.
Logical Expression of Full Adder
3.2.
Truth Table
4.
Difference between Half Adder and Full Adder
5.
Frequently Asked Questions
5.1.
What are adders and their types?
5.2.
What is the key difference between Half Adder and Full Adder?
5.3.
What are the advantages of a Full Adder over a Half Adder?
5.4.
What is the major difference between half adder and full adders quizlet?
5.5.
What is the difference between a full adder and a parallel adder?
6.
Conclusion