Digital Logic Operations

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In the field of digital electronics, many digital logic operations are performed which are considered as the fundamental building blocks. All the digital logic operations are based on the binary number system and Boolean algebra, where the data and information are represented in the form of binary 0s and 1s. Digital logic operations are used to manipulate the binary digits to perform various tasks.

In this chapter, we will learn about commonly used digital logic operations in the field of digital electronics. Here are some widely used digital logic operations −

• Arithmetic Operations
• Logical Operations
• Encoding and Decoding
• Multiplexing and Demultiplexing
• Code Conversion
• Comparison
• Counting
• Data Storage
• Data Transmission

Let’s discuss each of these digital logic operations in detail along with their applications.

Arithmetic Operations in Digital Electronics

Arithmetic operations are basic mathematical operations like addition, subtraction, multiplication, division, etc. In digital electronics, these arithmetic operations are performed using various digital circuits like adders, subtractors, multiplier, etc.

In digital electronic systems, the given numbers are first converted into binary format and then desired operations are performed on them.

Arithmetic operations are one of the fundamental operations performed using various digital electronic systems like microprocessors, calculators, microcontrollers, etc.

The following are the four main arithmetic operations performed by a digital system −

Addition

Addition is performed by using a digital logic circuit called adder. It adds two numbers and generates a sum and a carry as output. For example, if 8 and 5 are two numbers, then adder will produce a sum term 3 and a carry output 1.

Subtraction

The arithmetic operation subtraction is performed by using a digital logic circuit called subtractor. It performs the subtraction of two numbers and produces a difference term and a borrow term as output.

Multiplication

A digital circuit used to perform multiplication of two numbers is called a multiplier. It multiplies the given numbers and generates a product term as output.

Division

The division operation of two numbers is performed by using a digital circuit called divider. It performs division of two numbers and generates a quotient term and remainder term as output.

Logical Operations in Digital Electronics

Logical operations are used to compare two input parameters to make a decision. The commonly used logical operations in digital systems are OR, AND, NOT, NAND, NOR, XOR, and XNOR. All these logical operations are used to manipulate binary data to make crucial decisions in a digital system.

Logical operations are widely used for developing algorithms and conditional statements in programming.

Here are the commonly used logical operations in digital electronics −

AND

It is a basic logic operation performed by using a digital circuit called AND gate. In the AND operation, the output is true only if all of the inputs are true.

OR

OR is another basic logic operation in digital electronics. It is performed by using a digital logic circuit called OR gate. It produces a true output if any of the inputs are true.

NOT

NOT is a digital logic operation performed by using a circuit called NOT gate or inverter. It is also known as inversion operation. It generates a complement of the input.

NAND

NAND is a combination of AND and NOT operation. It is performed by using a digital circuit called NAND gate. The output of the NAND gate is false only if all of the inputs are true.

NOR

This logical operation is a combination of OR and NOT operations. It is performed by using a digital circuit called NOR gate. In the case of NOR operation, the output is false if any of the inputs are true.

XOR

The logical operation XOR or Exclusive OR is performed by using a digital logic circuit called XOR gate. In the case of XOR operation, the output is true if the number of true inputs is odd.

XNOR

The logical operation XNOR is a combination of XOR and NOT operations. It is performed by using a digital logic circuit called XNOR gate. In the case of XNOR gate, the output is true if all of the inputs are either true or false.

Encoding and Decoding in Digital Electronics

In digital electronics, encoding is a digital logic operation used to convert a familiar number or symbol into a coded format. A digital circuit called encoder is used to perform encoding, where the encoder receives digits, alphabets, and symbols and converts them into their respective binary codes.

On the other hand, decoding is the inverse operation of encoding. It is performed by using a digital logic circuit called decoder. Decoding is a digital logic operation that involves the conversion of a binary-coded information to other format like decimal, octal, hexadecimal, alphabets or symbols.

Both encoding and decoding are used in digital communication, error correction, data compression, etc.

Multiplexing and Demultiplexing in Digital Electronics

Multiplexing is a digital logic operation that combines multiple signals into a single signal. Hence, it is also termed as data sharing or selecting. A digital circuit called multiplexer is used to perform multiplexing. Multiplexing involves the process of switching information from multiple input lines on to a single output line in a specific sequence.

Demultiplexing is the reverse process of multiplexing. In the case of demultiplexing, information is switched from one input line on to multiple output lines. The digital circuit used to perform demultiplexing is called a demultiplexer.

Multiplexing and demultiplexing are two widely used digital logic operation in optimization of communication channels.

Code Conversion in Digital Electronics

Code conversion is a digital logic operation that involves converting information coded in one form to another form. It is performed by using a digital circuit called code converter.

Code conversion is an essential operation in interfacing between different digital systems. Some common examples of code converters are BCD to XS-3 converter, XS-3 to gray converter, etc.

Comparison Operation in Digital Electronics

Comparison is a digital logic operation performed using a digital circuit called comparator. The comparator compares two quantities and generates an output signal indicating whether the two input quantities are equal or not.

Counting Operation in Digital Electronics

Counting is a digital logic operation performed by using a digital circuit called counter. It involves the counting of increase or decrease in binary numbers.

Counting operation plays a vital role in various digital devices like memory, timers, digital clocks, microprocessors, etc. It is used to control the sequence of operation in a digital system.

Data Storage in Digital Electronics

Data storage is an essential operation in digital systems. It involves storing and retrieving digital data and information stored in the memory devices. Data storage can be performed using various digital storage devices like flip-flops, registers, memory units, etc.

Data Transmission in Digital Electronics

Data transmission is a digital logic operation in which binary data is transferred from one point to another in a digital system. In digital electronics, data transmission can be done either through wires or wireless channels.

Data transmission is a fundamental operation in digital communication where data is exchanged between different components of the system.

Conclusion

In conclusion, digital logic operations are used to manipulate binary data to perform various operations. They are considered as the fundamental building blocks of digital systems like microprocessors, microcontrollers, memory devices, communication systems, etc. Hence, it is essential to understand the digital logic operations for designing reliable digital systems and understand their behavior.

In this chapter, we covered all the essential digital logic operations along with their applications. In the next chapter, we will learn the advantages and limitations of digital systems.