Half Adder and Full Adder in Digital Electronics
Video Explanation: Half Adder and Full Adder
Watch this video for a clear and step-by-step explanation of the Half Adder and Full Adder, including logic diagrams, truth tables, and real-world applications in digital electronics.
Download Notes (PDF)
You can download the complete notes on Half Adder and Full Adder in PDF format for offline study and exam revision.
Adder Circuit (Digital Electronics)
An adder circuit is a combinational logic circuit used to perform the addition of binary numbers. Adders are the basic building blocks of arithmetic operations inside digital systems such as computers, calculators, and processors. Depending on the number of input bits and carry handling, adders are mainly classified into Half Adder and Full Adder.
1. Half Adder
A half adder is a combinational logic circuit that adds two single-bit binary numbers. It produces two outputs: Sum and Carry. It is called a “half” adder because it does not consider any carry input from a previous stage.
Inputs and Outputs
- Inputs: A, B
- Outputs: Sum (S), Carry (C)
Logic Expression
- Sum (S) = A ⊕ B (XOR operation)
- Carry (C) = A · B (AND operation)
Truth Table of Half Adder
| A | B | Sum (S) | Carry (C) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Logic Diagram Description
A half adder is implemented using one XOR gate to generate the Sum output and one AND gate to generate the Carry output.
Limitations of Half Adder
- It cannot add three bits at a time.
- There is no carry input.
- Not suitable for multi-bit binary addition.
2. Full Adder
A full adder is a combinational logic circuit that adds three binary inputs: two significant bits and one carry input from the previous stage. It produces two outputs — Sum and Carry out.
Inputs and Outputs
- Inputs: A, B, Carry-in (Cin)
- Outputs: Sum (S), Carry-out (Cout)
Logic Expressions
- Sum (S) = A ⊕ B ⊕ Cin
- Carry (Cout) = AB + BCin + ACin
Truth Table of Full Adder
| A | B | Cin | Sum (S) | Carry (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 |
Implementation of Full Adder Using Half Adders
A full adder can be constructed using two half adders and one OR gate. The first half adder adds inputs A and B. The second half adder adds the first sum with the carry input (Cin). The carry outputs are combined using an OR gate.
Applications of Adder Circuits
- Arithmetic Logic Unit (ALU)
- Digital calculators
- Microprocessors
- Binary counters
- Digital signal processing systems
Quick Summary
| Feature | Half Adder | Full Adder |
|---|---|---|
| Number of inputs | 2 | 3 |
| Carry input | No | Yes |
| Outputs | Sum, Carry | Sum, Carry |
| Logic gates used | XOR, AND | XOR, AND, OR |
| Used in | Basic addition | Multi-bit binary addition |
Download Notes PDF
Download the complete PDF notes on Half Adder and Full Adder for quick revision and exam preparation.
- Clear theory with diagrams
- Truth tables and logic expressions
- Exam-oriented questions
- Easy language for beginners
Tip: Save this PDF for quick revision before exams.