- Digital Electronics Tutorial
- Digital Electronics - Home
- Digital Electronics Basics
- Types of Digital Systems
- Types of Signals
- Logic Levels And Pulse Waveforms
- Digital System Components
- Digital Logic Operations
- Digital Systems Advantages
- Number Systems
- Number Systems
- Base Conversions
- Binary Numbers Representation
- Binary Arithmetic
- Signed Binary Arithmetic
- Octal Arithmetic
- Hexadecimal Arithmetic
- Complement Arithmetic
- Binary Codes
- Binary Codes
- 8421 BCD Code
- Excess-3 Code
- Gray Code
- ASCII Codes
- EBCDIC Code
- Code Conversion
- Error Detection & Correction Codes
- Logic Gates
- Logic Gates
- AND Gate
- OR Gate
- NOT Gate
- Universal Gates
- XOR Gate
- XNOR Gate
- CMOS Logic Gate
- Two Level Logic Realization
- Threshold Logic
- Boolean Algebra
- Boolean Algebra
- Laws of Boolean Algebra
- Boolean Functions
- DeMorgan's Theorem
- SOP and POS Form
- Minimization Techniques
- K-Map Minimization
- Three Variable K-Map
- Four Variable K-Map
- Five Variable K-Map
- Six Variable K-Map
- Don't Care Condition
- Quine-McCluskey Method
- Min Terms and Max Terms
- Canonical and Standard Form
- Max Term Representation
- Simplification using Boolean Algebra
- Combinational Logic Circuits
- Digital Combinational Circuits
- Digital Arithmetic Circuits
- Multiplexers
- Parity Bit Generator and Checker
- Comparators
- Encoders
- Keyboard Encoders
- Priority Encoders
- Decoders
- Demultiplexers
- Arithmetic Logic Unit
- 7-Segment LED Display
- Code Converters
- Code Converters
- Binary to Decimal Converter
- Decimal to BCD Converter
- BCD to Decimal Converter
- Binary to Gray Code Converter
- Gray Code to Binary Converter
- BCD to Excess-3 Converter
- Excess-3 to BCD Converter
- Adders
- Half Adders
- Full Adders
- Serial Adders
- Parallel Adders
- Full Adder using Half Adder
- Half Adder vs Full Adder
- Binary Adder-Subtractor
- Subtractors
- Half Subtractors
- Full Subtractors
- Parallel Subtractors
- Full Subtractor using 2 Half Subtractors
- Half Subtractor using NAND Gates
- Sequential Logic Circuits
- Digital Sequential Circuits
- Clock Signal and Triggering
- Latches
- Flip-Flops
- Conversion of Flip-Flops
- Shift Registers
- Shift Register Applications
- Counters
- Finite State Machines
- Algorithmic State Machines
- A/D and D/A Converters
- Analog-to-Digital Converter
- Digital-to-Analog Converter
- DAC and ADC ICs
- Realization of Logic Gates
- NOT Gate from NAND Gate
- OR Gate from NAND Gate
- AND Gate from NAND Gate
- NOR Gate from NAND Gate
- XOR Gate from NAND Gate
- XNOR Gate from NAND Gate
- NOT Gate from NOR Gate
- OR Gate from NOR Gate
- AND Gate from NOR Gate
- NAND Gate from NOR Gate
- XOR Gate from NOR Gate
- XNOR Gate from NOR Gate
- NAND/NOR Gate using CMOS
- Memory Devices
- Memory Devices
- RAM and ROM
- Cache Memory Design
- Programmable Logic Devices
- Programmable Logic Devices
- Programmable Logic Array
- Programmable Array Logic
- Field Programmable Gate Arrays
- Digital Electronics Families
- Digital Electronics Families
- CPU Architecture
- CPU Architecture
Half Adder in Digital Electronics
Addition is one of the most basic operations performed by different electronic devices like computers, calculators, etc. The electronic circuit that performs the addition of two or more numbers, more specifically binary numbers, is called as adder. Since, the logic circuits use binary number system to perform the operations, hence the adder is referred to as binary adder
Depending on the number of bits that the circuit can add, adders (or binary adders) are of two types −
- Half Adder
- Full Adder
In this article, we will discuss the half adder, its definition, circuit diagram, truth table, kmap, characteristic equations, and applications.
What is a Half-Adder?
A combinational logic circuit which is designed to add two binary digits is called as a half adder. The half adder provides the output along with a carry value (if any). The half adder circuit is designed by connecting an EX-OR gate and one AND gate. It has two input terminals and two output terminals for sum and carry. The block diagram and circuit diagram of a half adder are shown in Figure-1.
From the logic circuit diagram of half adder, it is clear that A and B are the two input bits, S is the output sum, and C is the output carry bit.
In the case of a half adder, the output of the EX-OR gate is the sum of two bits and the output of the AND gate is the carry. Although, the carry obtained in one addition will not be forwarded in the next addition because of this it is known as half adder.
Operation of Half Adder
Half adder adds two binary digits according to the rules of binary addition. These rules are as follows −
$$\mathrm{0 \: + \: 0 \: = \: 0}$$
$$\mathrm{0 \: + \: 1 \: = \: 1}$$
$$\mathrm{1 \: + \: 0 \: = \: 1}$$
$$\mathrm{1 \: + \: 1 \: = \: 10 \: (Sum \: = \: 0 \: \& \: Carry \: = \: 1)}$$
According to these rules of binary addition, we can see that the first three operations produce a sum whose length is one digit, whereas in the case of last operation (1 and 1), the sum consists of two digits. Here, the MSB (most significant bit) of this result is called a carry (which is 1) and the LSB (least significant bit) is called the sum (which is 0).
Truth Table of Half Adder
Truth table is one that gives the relationship between inputs and outputs of a logic circuit and explains the operation of the circuit. The following is the truth table of the half-adder −
Inputs | Outputs | ||
---|---|---|---|
A | B | S (Sum) | C (Carry) |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
K-Map for Half Adder
We can use the K-Map (Karnaugh Map), a method for simplifying Boolean algebra, to determine equations of the sum bit (S) and the output carry bit (C) of the half adder circuit.
The k-map for half adder circuit is shown in Figure-2.
Characteristic Equations of Half-Adder
The characteristic equations of half adder, i.e., equations of sum (S) and carry (C) are obtained according to the rules of binary addition. These equations are given below −
The sum (S) of the half-adder is the XOR of A and B. Thus,
$$\mathrm{Sum, \: S \: = \: A \: \oplus B \: = \: AB' \: + \: A'B }$$
The carry (C) of the half-adder is the AND of A and B. Therefore,
$$\mathrm{Carry, \: C \: = \: A \cdot B }$$
Applications of Half Adder
The following are some important applications of half adder −
- Half adder is used in ALU (Arithmetic Logic Unit) of computer processors to add binary bits.
- Half adder is used to realize full adder circuit.
- Half adder is used in calculators.
- Half adder is used to calculate addresses and tables.
Conclusion
From the above discussion, we can conclude that half adders are one of the basic arithmetic circuits used in different electronic devices to perform addition of two binary digits. The major drawback of a half adder is that it cannot add the carry obtained from the addition of the previous stage. To overcome this drawback, full adders are used in electronic systems.