## Digital Electronics

**Digital electronics** is a branch of electronics that deals with the manipulation of digital signals or discrete voltage levels representing binary values (0s and 1s). It involves the design, analysis, and implementation of digital circuits and systems using electronic devices like transistors, logic gates, flip-flops, and more.

## Number System

In a digital system, the system can understand only an optional number system. In these systems, numeric characters are used to represent different values depending on which index is calculated in the number system.

### Binary

Binary is a base-2 number system, which means it uses only two digits – 0 and 1 – to represent any number. In computing, binary is the language of the computer, since all data and instructions are ultimately represented in binary form.

### Decimal

Decimal is a base-10 number system, which means it uses ten digits – 0 to 9 – to represent any number. It is the most common number system used in everyday life.

### Octal

Octal is a base-8 number system, which means it uses eight digits – 0 to 7 – to represent any number. Octal is often used in computing as it is easy to convert from binary to octal and vice versa.

### Hexadecimal

Hexadecimal is a base-16 number system, which means it uses sixteen digits – 0 to 9 and A to F – to represent any number. Hexadecimal is also commonly used in computing, especially when representing memory addresses or color codes, as it allows large numbers to be represented with fewer digits compared to decimal or binary.

## Number System Conversion

Number systems are different styles of representing figures. The most generally used number systems are decimal, double, octal, and hexadecimal. Converting from one number system to another can be done using the following methods.

- Decimal to Binary.
- Binary to Decimal.
- Decimal to Octal.
- Octal to Decimal.
- Decimal to Hexadecimal.

## BCD Character Codes

BCD stands for Binary Coded Decimal, which is a way of representing decimal digits using binary digits. In BCD, each decimal digit is represented by a binary code, typically using four bits. The binary codes 0000 to 1001 represent the decimal digits 0 to 9, respectively.

For example, the decimal number 123 is represented in BCD as:

0001 0010 0011

Each of the decimal digits 1, 2, and 3 is represented by its corresponding BCD code.

BCD is often used in electronic systems for representing decimal numbers, especially in systems that require high precision or accuracy. BCD can be used in arithmetic operations, but it requires more complex circuitry than binary arithmetic. Therefore, BCD is often converted to binary before arithmetic operations are performed, and then converted back to BCD for display or storage.

## Excess-3

Redundancy-3 (or XS3) code is an unweighted code used to represent the code used to represent decimal numbers. A self-complementary Binary Coded Decimal (BCD) and number system with biased representation. This is especially important for arithmetic operations because it eliminates the drawback of using the 8421 BCD code to add two decimal digits to add two digits greater than 9.

## Gray Code

Gray code is a set of binary number systems, also known as reflected binary code. The reason this code is called a mirrored binary is that it compares the first N/2 values to the last N/2 values in reverse order. In this code, two consecutive values differ by one bit in binary. Gray code is used for common hardware-generated sequences of binary digits. These numbers cause ambiguity or errors when moving from one number to the next. This code simply solves this problem by changing only 1 bit when switching between numbers.

Gray codes are very lightweight weighted codes because they do not depend on the value of a number given in position. This code is also called cyclic variable code because the transition from one value to the next only changes one bit.

## ASCII

ASCII stands for American Standard Code for Information Interchange. ASCII codes are alphanumeric codes used to transmit data in digital computers. ASCII is a 7-bit code that can represent either 27 or 128 different characters. ASCII code consists of 3-bit groups and 4-bit codes.

- The ASCII Code is a 7 or 8-bit alphanumeric code.
- This code can represent 127 unique characters.
- The ASCII code starts from 00h to 7Fh. In this, the code from 00h to 1Fh is used for control characters, and the code from 20h to 7Fh is used for graphic symbols.
- The 8-bit code holds ASCII, which supports 256 symbols where math and graphic symbols are added.
- The range of the extended ASCII is 80h to FFh.

## 1’s Complement Representation

Among the number representation methods, the most used representation method in digital electronics is the binary system. Complementary is used to represent negative decimal numbers in binary form. In the case of binary numbers, various forms of complement are possible, but in the case of binary numbers, the 2’s complement of 1 and 2 is mainly used. For example, the 1’s complement of the binary number 1011001 is 0100110. You can find the two’s complement of a binary number by changing each bit (0 to 1, 1 to 0) and adding 1 to the least significant bit. For example, the two’s complement of the binary number 1011001 is (0100110) 1=0100111.

A logic circuit can also be implemented using a NOT gate to find the 1’s complement of a binary number. It uses a NOT gate for each bit of a binary number. Therefore, to implement a logic circuit for 5-bit one’s complement, 5 NOT gates are used.

## 2’s Complement Representation

Like 1’s complement, 2’s complement is also used to represent signed binary numbers. To find the 2’s complement of a binary number, first find the 1’s complement of the binary number, then add 1 to the least significant bit.

For example, to calculate the 2’s complement of 1011001, first find the 1’s complement of 0100110 and add 1 to the least significant bit. So adding 1 to the least significant bit gives (0100110) 1=0100111. You can also build logic circuits using OR, AND, and NOT gates. The logic circuit for finding the 2’s complement of a 5-bit binary number is.

## Logic Gates

Logic gates play an important role in circuit design and digital systems. A building block for digital systems and electronic circuits that always has only one output. These valves may have one input or more than one, but most valves have two inputs. Depending on the relationship between inputs and outputs, these gates are called AND gates, OR gates, NOT gates, etc.

There are different types of gates are as follow:

#### AND

An AND gate is a logic gate that produces an output signal only when all of its input signals are high. It is one of the basic logic gates and is widely used in digital circuits.

#### OR Gate

An OR gate is a digital sense gate that performs a logical OR operation. It takes two or further input signals and produces a single affair signal. The affair signal is “high” or “1” if any of the input signals are “high” or “1”. In other words, if at least one of the input signals is” high”, also the affair signal is” high”.

#### NOT Gate

A NOT gate, also known as an inverter, is a fundamental digital logic gate that has a single input and a single output. It performs the logical operation of negation or complementation, which means that it outputs the opposite value of its input.

#### NAND Gate

A NAND gate is a digital logic gate that has two or more inputs and one output. It is a combination of an AND gate followed by a NOT gate. In other words, the output of a NAND gate is the complement of the output of an AND gate.

#### NOR Gate

A NOR gate is a digital logic gate that has two or more inputs and one output. It is a combination of an OR gate followed by a NOT gate. In other words, the output of a NOR gate is the complement of the output of an OR gate.

#### XOR Gate

An XOR gate, also known as an exclusive-OR gate, is a digital logic gate that has two inputs and one output. The output of an XOR gate is high (1) if and only if the two inputs are different (one is 1 and the other is 0), otherwise, the output is low (0).

#### XNOR Gate

An XNOR gate, also known as an exclusive-NOR gate, is a digital logic gate that has two inputs and one output. The output of an XNOR gate is high (1) if and only if the two inputs are the same (both are 0 or both are 1), otherwise, the output is low (0).

## Logic Families

The main goal of Digital Designs is to create integrated circuits (ICs). The construction of a circuit, or the arrangement of circuit elements in a particular way, creates a particular logical family. The IC’s electrical characteristics are the same. That is, other parameters such as noise margin, fan in, fan out, etc. are the same.

## Transistor-Transistor Logic (TTL)

Transistor- Transistor sense( TTL) is a type of digital circuit design that uses bipolar junction transistors( BJTs) to apply sense functions. It was constructed in the 1960s and was extensively used in computers and other digital systems until the 1980s, when it was largely replaced by newer technologies similar as CMOS.

In TTL circuits, sense gates are enforced using bipolar junction transistors( BJTs) as the main switching rudiments. The affair of a gate is connected to one or further inputs of other gates, forming a network of connected gates that perform the asked sense function.

## Emitter-Coupled Logic (ECL)

Emitter-Coupled Logic (ECL) is a type of digital logic family that was first introduced in the 1950s by General Electric. ECL is a type of high-speed, high-performance logic family that is commonly used in applications such as telecommunications, data communications, and high-speed computing.

Unlike other digital logic families such as TTL and CMOS, ECL uses bipolar transistors instead of MOSFETs. ECL is also known as Current Mode Logic (CML) because it uses the current flowing through the transistors to perform logical operations.

## MOSFET Logic

MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) logic refers to a family of digital logic circuits that use MOSFETs as the switching elements. MOSFETs are three-terminal devices consisting of a gate, source, and drain. The gate is separated from the channel (which connects the source and drain) by a thin layer of oxide. The voltage applied to the gate controls the conductivity of the channel, allowing MOSFETs to function as switches.

## TTL Gates

TTL stands for Transistor-Transistor Logic, which is a type of digital logic circuit that uses bipolar junction transistors (BJTs) to implement logic gates. TTL gates are widely used in digital electronics because they offer high speed, low power consumption, and good noise immunity.

## Boolean Algebra

Logic symbols 0 and 1 are used to designate digital inputs or outputs. The symbols “1” and “0” can also be used for permanently open and closed digital circuits. A digital circuit may consist of several logic elements. A set of rules known as the laws of Boolean algebra were invented to perform logical operations with a minimum number of logic gates. These rules are used to reduce the number of logic gates that perform logic operations.

Boolean algebra is primarily used to simplify and analyze complex Boolean expressions. It is also called binary algebra because it only uses binary numbers. George Boole developed binary algebra in 1854.

## Boolean postulates and laws

Boolean postulates are fundamental principles that form the basis of Boolean algebra, which is a branch of mathematics that deals with logical operations on binary variables. These postulates are as follows:

- Identity Law.
- Commutative Law.
- Associative Law.
- Distributive Law.
- Complement Law.

## De-Morgan’s Theorem

The famous mathematician De Morgan invented two of the most important theorems in Boolean algebra. DeMorgan’s theorem is used to mathematically test the equivalence of NOR and negative AND gates, and negative OR and NAND gates. These theorems play an important role in solving various Boolean algebraic expressions. The table below defines the logical operation for each input variable combination.

The rules of De Morgan’s theorem are derived from Boolean expressions for OR, AND, and NOT using two input variables x and y. Demogan’s first theorem states that if you perform an AND operation on two input variables and then perform a NOT operation on the result, the result is equivalent to an OR operation on the complements of those variables. DeMorgan’s second theorem states that if you perform an OR operation on two input variables and then perform a NOT operation on the result, the result is equivalent to an AND operation on the complements of those variables.

## Principle of Duality

The principle of duality is a concept that appears in various fields, including mathematics, physics, and philosophy. In mathematics, the principle of duality states that for every true statement about a mathematical structure, there is another true statement obtained by interchanging certain pairs of words or symbols.

## Boolean Functions

Logic symbols 0 and 1 are used to designate digital inputs or outputs. The symbols “1” and “0” can also be used for permanently open and closed digital circuits. A digital circuit may consist of several logic elements. A set of rules known as the laws of Boolean algebra were invented to perform logical operations with a minimum number of logic gates. These rules are used to reduce the number of logic gates that perform logic operations.

Boolean algebra is primarily used to simplify and analyze complex Boolean expressions. It is also called binary algebra because it only uses binary numbers. George Boole developed binary algebra in 1854.

## Minimization of Boolean expressions

Minimization of Boolean expressions is the process of reducing a complex Boolean expression to its simplest form. The purpose of this process is to simplify the expression, making it easier to analyze and understand.

There are several methods for minimizing Boolean expressions, including the algebraic method, the Karnaugh map method, and the Quine-McCluskey method.

## Sum of Product

The Sum of Product expression is equivalent to the logical AND fuction which Sums two or more Products to produce an output

Boolean Algebra is a simple and effective way of representing the switching action of standard logic gates and a set of rules or laws have been invented to help reduce the number of logic gates needed to perform a particular logical operation. Sum-of-Product form is a Boolean Algebra expression in which different “product” terms from inputs are “summed” together.

## Product of Sum

In the article Sum of a Product, we explained that the sum of a product (SOP) expression is equivalent to a logical AND-OR function. Similarly, the expression Product of Sum (POS) is equivalent to the logical OR-AND function, meaning that it outputs the product (AND) of two or more sums (OR). A product of sum (POS) expression consists of multiple terms joined by OR, and finally combined by AND. The order of logical operations leads to the equivalent of the OR-AND function of sum product (POS).

## Minterm

minterm is a Boolean expression that evaluates to 1 for one cell and 0 for all other cells in the Karnaugh map or truth table. If the minterm has one 1 and the rest of the cells are 0, it will appear to cover the min area 1.

The plot on the top left shows the minterm ABC, the term for a single product, as a single 1 on the map. 0 otherwise. So far, the Karnot map has not shown zero. Omit it unless absolutely necessary.

## Maxterm

maxterm is a Boolean expression that evaluates to 0 for the expression in one cell of the Karnaugh map or truth table and 1 for all other cells. The top left plot shows maxterm(ABC), one term in the sum, as 1 on the map and 1 otherwise.

If maxterm has one 0 and the rest of the cells are 1, it appears to cover a maximum area of 1.

Now that we are dealing with the new maxterms, there are some differences. The max term in Karnaugh’s map is 0, not 1. In this example, the maximum term is the sum of terms (ABC), not the product term. It also seems odd that (ABC) maps to cell 000.

## Canonical Forms

In mathematics, a canonical form is a standard representation of a mathematical object, which is unique and independent of any particular context or coordinate system. Canonical forms are often used to simplify calculations, to identify and classify objects, and to establish a basis for further analysis.

## K-map Simplification with Don’t Care

Karnaugh maps, also known as K-maps, are used to simplify Boolean expressions. The map consists of a grid of squares, where each square represents a possible combination of input variables. The values of the output for each combination are represented by the corresponding square. K-maps can be used to simplify Boolean expressions by identifying groups of adjacent squares that have the same output value.

## Combinational circuits

Combinational circuits are digital circuits that perform Boolean logic operations on their inputs to produce an output. These circuits have no memory, which means that the output only depends on the current input.

Combinational circuits can be designed using logic gates, such as AND, OR, and NOT gates, and their derivatives, such as NAND and NOR gates. These gates are connected together in a way that produces the desired logical operation.

### Half Adder

A half-adder is a basic building block with two inputs and two outputs. An adder is used to perform an OR operation on two 1-bit binary numbers. Carry and sum are the two output states of the half adder.

### Full Adder

A half adder is used to add only two numbers. To overcome this, a full adder was developed. A full adder is used to add three 1-bit binary numbers A, B and a carry C. A full adder has three input states and two output states, sum and carry.

### Half Subtractors

A half subtractor is also a building block for subtracting two binary numbers. It has two inputs and two outputs. This circuit is used to subtract two 1-bit binary numbers A and B. “Difference” and “borrowed” are the two output states of the half-adder.

### Full Subtractors

A half subtractor is used to subtract only two numbers. Full subtractors have been developed to solve this problem. The full subtractor is used to subtract three 1-bit numbers A, B, and C, which are the minuend, subtract, and borrow, respectively. A full subtractor has three input states and two output states: diff and Borrow.

## Serial Adder/Subtractor

A serial adder/subtractor is a digital circuit that performs the addition and subtraction of binary numbers in a serial fashion, which means that the bits of the operands are processed one at a time. In other words, the addition or subtraction operation is carried out on the least significant bits (LSB) first, then propagates towards the most significant bits (MSB).

## Parallel Adder/Subtractor

A parallel adder/subtractor is a digital circuit that performs both addition and subtraction operations on binary numbers in parallel. In other words, it can perform these operations simultaneously on multiple bits of two binary numbers.

The most common type of parallel adder/subtractor is the 4-bit adder/subtractor, which has four inputs and two outputs. The four inputs are two 4-bit binary numbers A and B, and two control inputs C0 and C1, which determine whether the circuit performs addition or subtraction.

## BCD Adder/Subtractor

A BCD( Binary Coded Decimal) adder/ subtractor is a digital circuit that performs computation operations on decimal figures decoded in double form. BCD is a rendering scheme in which each decimal number is represented by a 4- bit double number.

## Decoder

A decoder is a digital circuit that takes a binary code as input and produces one or more output signals. The output of the decoder corresponds to a particular input code. Decoders are used to convert a binary code into a more meaningful form, such as a display on a digital screen or the activation of specific circuits in a computer system.

## Encoders

An encoder is a digital circuit that takes multiple input signals and produces a single output signal. The output of the encoder is a binary code that represents the input data. Encoders are used in digital communication systems, where data is transmitted over a communication channel. They are also used in error detection and correction systems, where the data needs to be encoded before transmission to ensure that it can be accurately decoded at the receiver.

## Multiplexer

A multiplexer, also known as a “mux,” is a device that allows multiple input signals to be selected and combined into a single output signal. In digital electronics, a multiplexer is often used to switch between multiple digital signals and to route them to a single output line, based on a control signal.

## Demultiplexer

A demultiplexer (DEMUX) is a digital circuit that takes a single input signal and distributes it to one of several output lines. Demultiplexers are used to separate a single data stream into multiple streams for processing by different circuits or devices. They are also used in digital communication systems to extract data from a single data stream transmitted over a communication channel.

## Sequential Circuits

The word “sequential circuit” means “a circuit whose output depends on the sequence or time of its inputs.”

So a series circuit consists of a Y input, a logic gate and an X output.

Sequential circuits produce outputs based on current input and previous input variables. So we can say that a series circuit can store binary information. This binary information provides the state of the series circuit at any given time. The block diagram of the sequential circuit is shown below.

## Latch

A latch is a type of electronic circuit that is used to store a bit of information. It is made up of a series of logic gates, and it can be used to store a 0 or a 1, which can then be retrieved later. Latches are commonly used in digital circuits and computer memory systems, where they play an important role in storing and retrieving data.

## SR Flip-Flops

SR flip-flops, also known as Set-Reset flip-flops, are digital circuits that store a single bit of data. They are commonly used in digital electronics, such as in memory and control circuits.

An SR flip- bomb has two inputs, labeled S and R, and two labors, labeled Q and Q’. When S is set to 1, the Q affair is set to 1, and when R is set to 1, the Q’ affair is set to 1. When both S and R are set to 0, the flip- bomb maintains its former state.

## Data

Data is usually stored in electronic storage devices such as hard drives, solid-state drives, or flash memory. The data can be accessed and processed using digital circuits such as logic gates, which perform basic operations such as AND, OR, and NOT on binary signals.

## Toggle

Toggle refers to the action of switching between two different states or options, typically by pressing a button or switch. Toggling can be used in a variety of contexts, such as toggling the power on or off on an electronic device, toggling between different modes on a software program, or toggling between two different settings on a physical device. The term “toggle” is also sometimes used as a noun to refer to the button or switch that is used to perform the toggling action.

## Synchronous

In synchronous transmission, data is sent in blocks or frames. This transmission is full-duplex. Synchronization is required between sender and receiver. In synchronous transmission, there are no gaps between data. It is more efficient and reliable than asynchronous transmission when transferring large amounts of data.

Example :

chatting

phone conversation

video meeting

## Asynchronous

In an asynchronous transfer, data is sent as bytes or characters. This transmission is a half-duplex transmission. In this transfer, a start bit and a stop bit are added to the data. No synchronization required.

Example :

Email Address

forum

letter

## Registers- Serial-in-Parallel-out

A serial-in-parallel-out register (SIPO) is a type of digital circuit that is used to convert a serial data stream into a parallel data stream. This type of register has a single input line, which receives data one bit at a time. The data is then shifted into the register and stored in a series of flip-flops. When all the bits have been shifted in, they can be outputted simultaneously in parallel form.

## Parallel-in-Serial-Out

Parallel-in-Serial-Out (PISO) is a type of shift register in digital electronics. It is a sequential logic circuit that takes in parallel input data and outputs the data serially, one bit at a time. The PISO shift register is often used in applications where multiple bits of data need to be transmitted or processed serially.

## Applications of Flip Flops

Flip-flops find applications in many areas of digital electronics. Flip-flops are the main components of sequential circuits. In particular, edge-triggered flip-flops are very unique devices that can be used in a wide range of applications, such as storing binary data, counters, and transferring binary data from one place to another. The flop is:

- Counters
- Registers
- Frequency Divider circuits
- Data transfer

All of these apps use trigger sync. Almost all of them fall under the category of sequential circuits.