Category: digital-electronics

Digital Electronics Tutorial Table of content Digital Electronics Tutorial What is Digital Electronics? Applications of Digital Electronics Digital Electronics Important in Computer Organization Audience Prerequisites FAQs about Digital Electronics PDF Version Quick Guide Resources Job Search Discussion Digital Electronics Tutorial This is a comprehensive tutorial on Digital Electronics. You can use this tutorial to learn the following topics − Basics of digital signals and systems Different types of number systems and their conversions Binary codes and their conversions Boolean functions and their minimization Implementation of Boolean expressions Combinational logic circuits and their applications Sequential circuits and their applications Memory devices Logic Families The topics covered in this tutorial are relevant in various technical exams like GATE, engineering services exams, university exams, and various other competitive exams. Also, you can use the knowledge gained in this tutorial in different industrial applications such as PLC programming, software development, embedded system design, control and automation system design, and more. What is Digital Electronics? Digital electronics is a subdomain in electrical and electronics engineering that deals with the study of digital signals and systems, processing of digital signals and their applications. Under digital electronics, several important concepts are covered such as logic gates, Boolean operations, logic functions, combinational circuits, sequential circuits, logic families, and more. Digital electronics plays a vital role in a wide range of practical applications such as computers, communication systems, consumer electronics, automation and control systems, and many other fields that rely on digital signals. Applications of Digital Electronics The knowledge of Digital Electronics plays an indispensable role in several important fields such as computer science and information technology, communication systems, telecom networks, wireless communication, consumer electronics like TV, smartphones, laptops, etc., medical equipment, and industrial automation and robotics engineering. Digital Electronics Important in Computer Organization Computer organization is a branch of computer engineering that deals with the study of the physical components of a computer system and their functioning. It allows us to understand how different components of a computer system interact with each other to process data instructions and perform tasks. Under computer organization, we study about the hardware architecture and design principles of a computer system. Therefore, computer organization helps computer engineers and system designers to develop more efficient computer systems. Here are the key points that highlight the importance of Digital Electronics in the field of Computer Organization − The binary representation of digital electronics is used to design different circuits of a computer system. Digital electronics provide logic gates and other digital circuits which are used in designing different components of a computer system like control units, arithmetic logic units (ALUs), memory unit, and more. Digital electronics provide principles for design memory units and data storage systems in computers. Digital electronics principles also empower computers to perform various digital signal processing tasks such as modulation, demodulation, filtering, etc. Digital electronics is the fundamental building block of computer organization which provides all the important tools and techniques required for designing and implementing circuits and systems of a computer. Audience This tutorial is a complete reference for digital electronics enthusiasts. Anyone who wants to understand the basics and implementation of digital circuits can go through this tutorial and can excel his/her digital electronics skills. Prerequisites This tutorial is so designed that anyone with a basic knowledge on the initial concepts of Digital Electronics can understand the topics covered in this tutorial without the need of any parallel resource. FAQs about Digital Electronics There are some very Frequently Asked Questions(FAQ) about Digital Electronics, this section tries to answer them briefly. How does Digital Electronics differ from Analog Electronics? The primary difference between digital and analog electronics is that digital electronics process data in the form of discrete or discontinuous time signals, while analog electronics use continuous signals for processing purposes. What are the Advantages of Digital Electronics Over Analog Electronics? Some of the key advantages of digital electronics over analog electronics are listed here − Digital electronic systems are more precise and accurate as compared to analog electronic system. Digital electronic systems can process, store, and transmit signals and information more efficiently. Digital signals and systems are highly immune against noise and interferences. Digital systems can be programmed and reprogrammed easily to meet the requirements of a specific application, on the other hand analog systems require changes at hardware level. Digital systems are highly cost-effective and also scalable. What are Logic Gates and How are They Used in Digital Electronics? Logic gates are digital circuits used as the fundamental building blocks in digital system designs. They are binary devices that perform logical operations on inputs as per a predefined set of functions. In digital electronics, seven common logic gates are widely used and they are AND gate, OR, gate, NOT gate, NAND gate, NOR gate, XOR gate, and XNOR gate. They are used to design and implement the following − Boolean functions and expressions Arithmetic operations like addition, subtraction, etc. Combination circuit design such as multiplexers, demultiplexers, encode, decoder, etc. Sequential circuit design like counters, flip-flops, registers, timers, etc. Memory devices and many more digital systems. What is the Significance of Boolean Algebra in Digital Electronics? Boolean algebra is an important tool used in digital electronics. It provides a mathematical framework to perform data manipulation in binary format. Boolean algebra provides a complete set of laws and operations to simplify complex logical expressions and implement optimized digital systems.

Digital Electronics – K-Map Minimization ”; Previous Next What is Karnaugh Map? In realization of digital electronic systems, the simplification of Boolean expressions is one of the most crucial steps because it reduces the hardware complexity and cost of production. There are several tools and methods available for simplifying complex Boolean expression. K-Map or Karnaugh Map is one of such simplification methods. K-Map was developed by Maurice Karnaugh in the year of 1953. It is a visual or graphical method used to simplify the Boolean expressions. K-Map is one of the most efficient simplification tools when the number of variables in the Boolean expression are less than or equal to four. However, for five, six, and more variables, the K-Map becomes quite difficult. The K-Map or Karnaugh map makes the use of two dimensional table for simplification of the Boolean functions. The size of this table increases considerably with the increase in the number of variables in the Boolean functions. Some typical examples of K-Map of two variable, three variable, and four variables are shown in Figure-1. From Figure-1, it is clear that the number of squares or cells in the Karnaugh map depends on the number of variables in the expression. If n is the number of variables in the given Boolean function, then the corresponding Karnaugh map (K-Map) will have 2n squares or cells. For examples, if the number of variables in the Boolean function is 3, then the corresponding K-Map will have 8 (= 23) cells. Structure of Karnaugh Map All the Karnaugh maps or K-Maps have a generalized similar structure as shown in Figure-1. A typical K-Map has a table of certain cells. On the top-left corner of this table, a set of variables are represented as A, B, C, D. These variables are basically the input variables involved in the logical expression that requires to be simplified. The values of these inputs variables in binary form are represented along their respective sides, i.e., on the top and left of the table. From the above examples, it can be observed that the binary numbers along the top and left of the K-Map are not in their normal binary order, instead they are in the gray code. The Gray code is used to ensure that the two physically adjacent cells are actually adjacent. This makes the process of grouping easier during minimization of the Boolean expression. For providing simplicity in reading the K-Map, each cell of the K-Map is assigned a decimal number represented at the bottom-right corner of the cell. For example, in the three variable K-map (figure-1), the second cell of the K-Map represents a bit pattern 001, hence this cell is represented by its decimal equivalent 1. K-Map Simplification The procedure of K-Map or Karnaugh map simplification is started with the entering the values of the variables, either in their SOP (Sum of Products) form or in POS (Product of Sums) form, in the right K-map cells. After that we need to group the maximum number of 1s (in the case of SOP form) or the maximum number of 0s (in the case of POS form). Each of these groups must be in powers of 2 and must be carried on in decreasing order only. Once the grouping is done, each group has to be expressed in terms of combinations of input variables which are corresponding to the common binary values along the associated rows and columns. At last, all the combinations express the output expression of the Boolean function. Advantages of Karnaugh Map The following are the important advantages of the Karnaugh map − For simplifying Boolean expression, the K-map does not require the knowledge of theorems of Boolean algebra. Karnaugh map involves less number of steps in simplification process of logical expressions as compared to other simplification techniques. Limitations of Karnaugh Map The following are the major limitations of the Karnaugh map − The most significant limitation of the Karnaugh map is that it is only efficient when the Boolean expression has less number of variables. It becomes quite complicated with the higher number of variables in the logical expression. The simplification of a Boolean function having more than or equal to five variables using K-Map is quite complex. It is very difficult to get equations correct with more than 5 variables using the K-map. Conclusion The Karnaugh map or K-Map is an efficient tool for simplifying Boolean expression up to 4 variables. It is an easy method for simplification of logic expression because it does not make the use of Boolean algebra theorems. Another advantage of K-Map is that it is a visual method of simplification. However, the K-map becomes complex and inefficient when the variables in the logical expression are equal to or more than 5. Print Page Previous Next Advertisements ”;

Types of Digital Systems ”; Previous Next A system is defined as a group of various components interconnected together to perform a specific task. For example, a digital computer consists of several components such as monitor, CPU (Central Processing Unit), memory, keyboard, mouse, printer, and more. All these components are connected together to accomplish certain tasks. Hence, a computer can be termed as a system. We can broadly classify systems into the following two categories − Analog Systems Digital Systems An analog system is a type of system that operates on continuous time signals, while a digital system is one that can work on discrete time signals. Read this chapter to learn the basics of digital systems and their types. What is a Digital System? A type of electronic system that is designed to store, manipulate, and communicate digitally represented information is termed as a digital system. Some common examples of digital systems include smartphone, laptops, smartwatch, tablet, desktop computers, etc. The working of a digital system is entirely based on digital signals or binary signals. Where, a digital signal is a type of signal that is represented as a discrete-elements. It can have two possible states namely high or low. The high state is denoted by the logic 1 and the low state is denoted by the logic 0. In a digital system, if the state of the signal is logic 1, the system will be on, and if the state of the signal is 0, the system will be off. Characteristics of Digital Systems Today, digital systems are widely used in almost every aspect of life. This is because of their high reliability and efficiency. The following are some key characteristics of digital systems − Digital systems are relative less complex to implement as they use binary number system having only two digits to represent the state of a system. In digital systems, the information is represented in the form of a group of 0s and 1s i.e., bits. This is called binary or digital representation of information. Digital systems rely on digital signals having two well-defined discrete states. This makes digital systems more reliable and efficient in terms of processing, storage, and communication of information. Digital systems use logical mathematics and operations to perform computing tasks. Digital systems can be manufactured in the form of integrated circuits (ICs) of very small sizes. Digital systems can be easily programmed to perform repeated tasks that reduces human efforts and cost. Digital systems are highly immune to noise and distortions. Types of Digital Systems Digital systems can be classified based on various parameters. Here are some important types of digital systems that we commonly use in practice − Combinational Digital Systems A combinational logic circuit or system is a type of digital circuit that performs logical operations and produces output depending on the present inputs. Hence, the output of a combinational digital circuit does not depend on the past inputs and outputs of the system. Example − The common examples of combinational digital systems are binary adders, subtractors, logic gates, multiplexers, demultiplexers, etc. Sequential Digital Systems A type of digital system that has a memory element to store past history of the system operation is called a sequential digital system. Therefore, the output of a digital system depends on both present inputs and past outputs of the system. Example of sequential digital systems are flip-flops, registers, memory devices, counters, etc. Programmable Logic Devices (PLDs) A programmable logic device is one that can be programmed to perform a specific task automatically. Example of programmable logic devices are microcontrollers, PLCs, etc. Digital Communication Systems A digital communication system is a type of digital system used for transmission and reception of information in the form of digital signals. Example of digital communication systems are internet, intranet, mobile communication system, Wi-Fi, etc. Digital Control Systems A digital control system is a computerized control system used to monitor and regulate the behavior of a dynamic system. Example − Digital control systems are extensively used in robotics, industrial automation, etc. Conclusion In conclusion, digital systems are modern systems known for their high speed and reliability. A digital system utilizes digital signals to store, process, and communicate the information. In this chapter, we explained the basics of digital systems and their types. Traverse to the next chapter to learn all about the types of signals used in the field of electronics engineering. Print Page Previous Next Advertisements ”;

Digital Electronics – Binary Arithmetic ”; Previous Next Binary arithmetic is one of the fundamental concepts in the field of digital electronics and computer engineering. It is basically the mathematics of binary numbers allow to perform various arithmetic operations on binary numbers. We know that the binary number system has two digits, i.e., 0 and 1 which are used to represent the ON or OFF states of the digital systems. Hence, binary arithmetic forms the foundation of the digital computing. In this chapter, we will discuss the following four main binary arithmetic operations − Binary Addition Binary Subtraction Binary Multiplication Binary Division Let’s discuss each of these binary arithmetic operations in detail along with solved examples. Binary Addition In binary arithmetic, the process of adding two binary numbers is called binary addition. Where, the binary numbers consist of only 0 and 1. In the binary addition, a carry is generated when the sum is greater than 1. Rules of Binary Addition The addition of two binary numbers is performed according to these rules of binary arithmetic − 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 (Sum = 0 & Carry = 1) Let us consider some examples to understand the binary addition. Example 1 Add two binary numbers, 1101 and 1110. Solution The binary addition of the given binary numbers is described below − Explanation Add 1 (rightmost bit of first number) and 0 (rightmost bit of the second number). It gives 1 + 0 = 1 (thus, write down 1 as sum bit). Add 0 (second rightmost bit of first number) and 1 (second rightmost bit of the second number). It gives 0 + 1 = 1 (write down 1 as sum bit). Add 1 (third rightmost bit of first number) and 1 (third rightmost bit of second number). It gives 1 + 1 = 10 (write down 0 as sum and 1 as carry). Add 1 (leftmost bit of the first number), 1 (leftmost bit of second number) and 1 (carry). It gives 1 + 1 + 1 = 11 (write down 1 as sum and 1 as carry). Write the end around carry 1 in the sum. Thus, the result is 11011. Example 2 Add 1010 and 11011. Solution The binary addition of given numbers is explained below − Explanation Add 0 (rightmost bit of first number) and 1 (rightmost bit of second number). It gives 0 + 1 = 1 (write down 1 as sum). Add 1 (second rightmost bit of first number) and 1 (second rightmost bit of second number). It gives 1 + 1 = 10 (write down 0 as sum and 1 as carry). Add 0 (third rightmost bit of first number), 0 (third rightmost bit of second number), and 1 (carry). It gives 0 + 0 + 1 = 1 (write down 1 as sum). Add 1 (leftmost bit of first number) and 1 (second leftmost bit of second number). It gives 1 + 1 = 10 (write down 0 as sum and 1 as carry). Add 1 (leftmost bit of second number) and 1 carry. It gives 1 + 1 = 10 (write down 0 as sum and 1 as the end around carry). Hence, the sum of 1010 and 11011 is 100101. Binary Subtraction In binary arithmetic, binary subtraction is a mathematical operation used to find the difference between two binary numbers. In binary subtraction, each bit of the binary numbers is subtracted, starting from the rightmost bit. Also, a borrow bit can be taken from higher bits if require. Rules of Binary Subtraction The binary subtraction is performed as per the following rules of binary arithmetic − 0 – 0 = 0 1 – 0 = 1 0 – 1 = 1 (borrow 1 from the next higher bit) 1 – 1 = 0 Let us see some examples to understand the binary subtraction. Example 1 Subtract 1100 from 1101. Solution The subtraction of given binary numbers is given below − 1101 – 1100 = 0001 Explanation Subtract 0 (rightmost bit of second number) from 1 (rightmost bit of first number). It gives 1 – 0 = 1 (write down 1 as difference). Subtract 0 (second rightmost bit of second number) from 0 (second rightmost bit of first number). It gives 0 – 0 = 0 as result. Subtract 1 (third rightmost bit of second number) from 1 (third rightmost bit of first number). It gives 1 – 1 = 0 as result. Subtract 1 (leftmost bit of second number) from 1 (leftmost bit of first number). It gives 1 – 1 = 0 as result. Thus, the difference of 1101 and 1100 is 0001. Example 2 Subtract 101 from 1111. Solution The subtraction of given binary numbers is explained below − Explanation Subtract rightmost bits: 1 – 1 = 0 Subtract second rightmost bits: 1 – 1 = 1 Subtract third rightmost bits: 1 – 1 = 0 Subtract leftmost bits: 1 – 0 = 1 Thus, the result is 1010. Example 3 Subtract 1011 from 1101. Solution The binary subtraction of 1101 and 1011 is given below − Explanation Subtract rightmost bits: 1 – 1 = 0. Subtract second rightmost bits: 0 – 1 = 1. A borrow 1 is taken from the next higher bit. Subtract third rightmost bits: 0 – 0 = 0. The 1 borrow is given

XNOR Gate in Digital Electronics ”; Previous Next An XNOR gate is a type of derived logic gate which is a combination of an XOR gate and a NOT gate. Hence, it produces a “NOTed XOR” output. In this chapter, we will explain the basic theory of XNOR logic gate, its working, circuit diagrams, and applications. So, let’s start with the basic definition of XNOR gate. What is XNOR Gate? The XNOR gate is a logic gate that has two inputs and one output. The output of the XNOR gate is high, only when both of its inputs same, i.e., either both inputs are high or both inputs are low. If the inputs are dissimilar, i.e., one is high and the other low, the output is low or logic 0. Since the XNOR gate produces a high output when both its inputs are similar, it is also known as an equality detector. The XNOR gate is also known as Exclusive-NOR or Ex-NOR gate. Actually, the XNOR gate is a combination of two logic gates namely, XOR gate and NOT gate. Therefore, XNOR Gate = XOR Gate + NOT Gate It is important remember that there is no such thing like an XNOR gate with three or more inputs. To obtain an XNOR gate with inputs more than two, we combine multiple two-input XNOR gates together. Logic Symbol of XNOR Gate The logic symbol for a two input XNOR gate is shown in the following figure. The bubble on the right-end represents the NOT operation. The variables A and B represent the input lines while Y represents the output line. Truth Table of XNOR Gate The truth table of an XNOR gate provides information about the operation and relationship between inputs and output of it. The truth table of a two-input XNOR gate is given below − Input Output A B Y 0 0 1 0 1 0 1 0 0 1 1 1 From this truth table, it can be observed that the XNOR gate produces a high or logic 1 output when both of its inputs are same i.e., 0 and 0 or 1 and 1. Otherwise, it gives a low or logic 0 output. Boolean Expression of XNOR Gate The Boolean expression is a logical function that describes the relationship between inputs and output of an XNOR gate mathematically. The Boolean expression of a two-input XNOR gate is given below − $$\mathrm{Y \: = \: A \: \odot \: B}$$ This can also be expressed as, $$\mathrm{Y \: = \: AB \: + \: \bar{AB}}$$ Here, A and B are input variables while Y is the output variable. Working of XNOR Gate The operation of a two-input XNOR gate for different input combinations is explained below − If A = 0 and B = 0, the output of the XNOR gate is Y = 1. If A = 0 and B = 1, the output of the XNOR gate is Y = 0. If A = 1 and B = 0, the output of the XNOR gate is Y = 0. If A = 1 and B = 1, the output of the XNOR gate is Y = 1. Hence, we can see that the output is high or logic 1 for similar inputs. It is low or logic 0 for dissimilar inputs. XNOR Gate using Switches We can realize the XNOR gate logic with the help of two switches, a battery, and a lamp. Here is the electrical circuit representing the XNOR logic gate. In this circuit, when both switches A and B are at same level i.e., at 0 and 0 or 1 and 1. There is a closed path for the current to flow through the lamp. This turns on the lamp and represents the high or logic 1 output. If the switches are at different levels i.e., one is at level 0 and the other is at level 1. There is no complete path between the battery and lamp. Hence, the lamp will not glow and represent the low or logic 0 output. Hence, the above shown switching circuit implements the XNOR logic operation. XNOR Gate as an Inverter The XNOR gate can operate as an inverter. If we connect one of the input lines of the XNOR gate at low or logic 0 signal and we apply the input signal to another input line. Then, the output of the XNOR gate will be the complement of the input applied. The logic circuit of an XNOR gate working as an inverter is depicted in the following figure. We can also explain this operation with the help of its Boolean expression as below. $$\mathrm{Y \: = \: AB \: + \: \bar{AB}}$$ If B is set at logic 0, then $$\mathrm{Y \: = \: A\cdot0 \: + \: \bar{A}\cdot1 \: = \: \bar{A}}$$ Hence, if one input XNOR gate is tied to logic 0, then the gate will work as an inverter. XNOR Gate as a Buffer The XNOR gate can also operate as a buffer. If we connect of one of the inputs of the XNOR gate to logic 1 and the input signal is applied to another input line. The output of the XNOR gate will be same as the input applied, i.e., the XNOR gate will work as a buffer. The XNOR gate working as a buffer is shown in the following figure. Logically, we can prove this

AND Gate in Digital Electronics ”; Previous Next In digital electronics, there are several different types of logic gates such as AND gate, OR gate, NOT gate, etc. In this chapter, we will explain the theory of AND gate. An AND gate is a basic logic gate used to implement various complex digital circuits and systems. The AND gate performs the logical multiplication of inputs applied to it and produces an output accordingly. What is an AND Gate? An AND gate is a type of basic logic gate used in various digital circuits and systems. It produces a high or logic 1 or True output, only when all its inputs are high or logic 1 or true. For all other combinations of inputs, it produces a low or logic 0 or False output. The logic symbols for the two and three input AND gates are depicted in the following figure. Here, A, B, and C are the input variables and Y is the output variable. In this chapter, we will cover AND gates having three inputs only. But we can design an AND gate for any number of input variables. Truth Table of AND Gate The truth table of an AND gate contains inputs and outputs, and specifies the relationship between them. The truth table of a two-input AND gate is given below − Input Output A B Y 0 0 0 0 1 0 1 0 0 1 1 1 From this truth table of two-input AND gate, it can be observed that the output of the AND gate is logic 1 or high, only when both inputs are logic 1 or high. The following table represents the truth table of a three-input AND gate − Input Output A B C Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 This truth table shows that the output is high or logic 1 only when all the three inputs to the AND gate are high or logic 1. For rest input combinations, the output is low or logic 0. From these truth tables of AND gate, we can conclude that an AND gate produces a high or logic 1 output, only when all its inputs are high or logic 1, otherwise the output is low or logic 0. Working of AND Gate The working of a two-input AND gate is explained below − If A = 0 and B = 0, the output is low i.e., Y = 0. If A = 0 and B = 1, the output is low i.e., Y = 0. If A = 1 and B = 0, the output is low i.e., Y = 0. If A = 1 and B = 1, the output is high i.e., Y = 1. The working of a three-input AND gate is explained below − If A = 0, B = 0, and C = 0, the output is low i.e., Y = 0. If A = 0, B = 0, and C = 1, the output is low i.e., Y = 0. If A = 0, B = 1, and C = 0, the output is low i.e., Y = 0. If A = 0, B = 1, and C = 1, the output is low i.e., Y = 0. If A = 1, B = 0, and C = 0, the output is low i.e., Y = 0. If A = 1, B = 0, and C = 1, the output is low i.e., Y = 0. If A = 1, B = 1, and C = 0, the output is low i.e., Y = 0. If A = 1, B = 1, and C = 1, the output is high i.e., Y = 1. This is all about working of a two-input and a three-input AND gates. Boolean Expression of AND Gate Boolean expression is a logic equation or a logic function that represents the mathematical relationship between inputs and output of the AND gate. The Boolean expression of a two-input AND gate is given by, Y = A · B Where, A and B are inputs and Y is the output. This expression is read as “Y is equal to A AND B.” The dot (·) symbol represents the AND operation. For the three-input AND gate, the Boolean expression is given by, Y = A · B · C It is read as “Y is equal to A AND B AND C”. In the same way, we can obtain the Boolean expression for an AND gate having any number of input variables. AND Gate using Transistor The transistor circuit of a two-input AND gate is shown in the following figure. The implementation of AND gate using transistors requires as many transistors as the number of inputs. For example, a two-input AND gate requires two transistors. Working of Transistor AND Gate The working the transistor AND gate shown in the above figure is explained below − When both

OR Gate in Digital Electronics ”; Previous Next In digital electronics, an OR Gate is a basic logic gate having two or more input lines and one output line. It performs the Boolean addition function. In this chapter, we will explain the theory of the OR gate. Here, we will cover the definition of OR gate, its logic symbol, Boolean expression, truth table, operation, and circuits. So, let’s get started with the basic definition of OR gate. What is an OR Gate? An OR gate is a type of logic gate used to perform logical addition. It can have two or more inputs and one output. The output of the OR gate is low or logic 0 only when all its inputs are low or logic 0. For rest input combinations, the output of the OR gate is high or logic 1. The logic symbols for a two-input and a three-input OR gate are shown in the following figure. Here, A, B, and C are the input lines and Y is the output line. Truth Table of OR Gate The truth table is a table that shows the relationship between different input combinations and output. The following is the truth table for a two-input OR gate − Input Output A B Y 0 0 0 0 1 1 1 0 1 1 1 1 The following table shows the truth table for a three-input OR gate − Input Output A B C Y 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 From these two truth tables, we can observe that the output of the OR gate is logic 0 or low, only when all the inputs to the OR gate are logic 0 or low. Otherwise, the output of the OR gate is high or logic 1. Boolean Expression of OR Gate The Boolean expression is a logical function that describes the mathematical relationship between inputs and output of the OR gate. The Boolean expression of a two-input OR gate is given below − Y = A + B Here, A and B are input variables and Y is the output variable. This expression is read as “Y is equal to A OR B”. Here, the “+” sign represents the OR operation. Similarly, the Boolean expression of a three-input OR gate is given below − Y = A + B + C Here, A, B, and C are the inputs and Y is the output. In the same way, we can extend this expression to any number of input variables. Working of OR Gate The operation of a two input OR gate for different input combinations is described below − If A = 0 and B = 0, the output of the OR gate is Y = 0. If A = 0 and B = 1, the output of the OR gate is Y = 1. If A = 1 and B = 0, the output of the OR gate is Y = 1. If A = 1 and B = 1, the output of the OR gate is Y = 1. This theory explains that when both inputs applied to an OR gate are low or logic 0, the output of the OR gate is also low or logic 0, otherwise it is high or logic 1. Similarly, the working of a three-input OR gate is described below − If A = 0, B = 0, and C = 0, the output of the OR gate is Y = 0. If A = 0, B = 0, and C = 1, the output of the OR gate is Y = 1. If A = 0, B = 1, and C = 0, the output of the OR gate is Y = 1. If A = 0, B = 1, and C = 1, the output of the OR gate is Y = 1. If A = 1, B = 0, and C = 0, the output of the OR gate is Y = 1. If A = 1, B = 0, and C = 1, the output of the OR gate is Y = 1. If A = 1, B = 1, and C = 0, the output of the OR gate is Y = 1. If A = 1, B = 1, and C = 1, the output of the OR gate is Y = 1. This theory also explains that the output of an OR gate is low or logic 0, only when all the three inputs are low or logic 0. OR Gate using Transistors We can implement the OR gate logic circuit using transistors. The implementation of a two-input OR gate using BJT transistors is shown in the following figure. This OR gate circuit is also referred to as transistor-transistor logic (TTL) OR gate. Working of Transistor OR Gate The operation of the above shown transistor OR gate circuit is explained below − When both inputs A and B

CMOS Logic Gate in Digital Electronics ”; Previous Next What is a Logic Gate? In digital circuits, a logic gate is a fundamental element of the digital circuit or system, that performs a specific logical operation. A logic gates typically has one or more inputs and only one output. The output of the logic gate is related to the inputs based on a certain logic. Some commonly used logic gates are: AND Gate, OR Gate, NOT Gate, NAND Gate, and NOR Gate. What is CMOS Technology? CMOS, Complementary Metal Oxide Semiconductor, is a predominant technology used for manufacturing integrated circuits (ICs). This technology is widely used for manufacturing a variety of digital electronic components like microprocessors, sensors, logic gates, and more. CMOS technology employs both NMOS (N-Channel Metal Oxide Semiconductor) and PMOS (P-Channel Metal Oxide Semiconductor) logic to implement different types of digital functions. CMOS technology is widely being used in realizing digital logic gates due to its key advantages, such as fast switching speed, low power consumption, high voltage range, high noise margins, etc. Basic CMOS Logic Gates Let us now discuss the basic CMOS logic gates in detail. CMOS OR Gate The OR gate is a basic logic gate in digital electronics. OR gates produce a high or logic 1 output when any of its inputs is high, and it produces a low or logic 0 output when all of its inputs are low. The truth table of a two-input OR gate is given below. Input Output A B Y = A + B 0 0 0 0 1 1 1 0 1 1 1 1 The implementation of a two input OR gate in CMOS logic is shown in the following figure. Here, we have combined multiple CMOS inverters together to build a CMOS OR gate. In the circuit diagram, the CMOS OR gate consists of a PMOS transistor and an NMOS transistor, which are joined in parallel fashion between the power supply voltage (V) and the output. In the above circuit, when one or both inputs (A and B) are high (logic 1), the corresponding PMOS and NMOS transistors switch in a way that the current flows from the output to ground, causes a low voltage (logic 0) at the output terminal. When both inputs are low (logic 0), the corresponding CMOS transistors switch in a way that the output is connected to the supply voltage, causing a high voltage (logic 1) at the output terminal. CMOS AND Gate The AND gate is a basic logic gate used in a variety of digital logic circuits. AND gate produces a high or logic 1 output only when all of its inputs are high, it produces a low or logic 0 output when any of its inputs is low. The truth table of the two-input AND gate is given below. Input Output A B Y = AB 0 0 0 0 1 0 1 0 0 1 1 1 The implementation of AND gate using CMOS technology is shown in the following figure. Here, to implement the CMOS AND gate, we have connected multiple CMOS inverters together. In the CMOS AND gate circuit, PMOS and NMOS transistors are used to build it. These transistors are connected in series between supply voltage (V) and the output (Y), and in parallel between the output and ground respectively. In the case of CMOS AND gate shown in the above figure, when both inputs are high (logic 1), the CMOS transistors switch in such a way that the output is connected to the power supply voltage (V), producing a high (logic 1) output. When any of its inputs is low, the CMOS transistors in the circuit switch such that the current flows from power supply to the ground, making output low (logic 0). CMOS NOT Gate A NOT gate is also a basic logic gate used in digital logic circuits. The NOT has a single input and a single output. The output of the NOT gate is high or logic 1 when its input is low or logic 0, and its output is low or logic 0 when its input is high or logic 1. In CMOS logic gates, the CMOS NOT gate is the simplest CMOS logic gate. It is also called CMOS Inverter Gate. The truth table of the NOT gate is given below. Input Output A Y = A” 0 1 1 0 The implementation of a NOT gate in CMOS technology is shown in the following figure. Here, the input is applied to the gate terminal of the two CMOS transistor, and the output is connected to their drain terminals. When a positive voltage pulse (logic 1) is applied to the input Vi, the CMOS transistor Q1 is off and the CMOS transistor Q2 is on. Therefore, the output voltage will be at ground voltage, i.e. logic 0. When the ground voltage (logic 0) is applied to the input Vi, the CMOS transistor Q1 is on and the CMOS transistor Q2 is off. Thus, the output will be closed to +V, i.e. logic 1. Print Page Previous Next Advertisements ”;

Components of Digital System ”; Previous Next A digital system is a type of electronic system used to store, process, and manipulate data represented in the form of digital signals, where a digital signal is a discrete time signal. Digital systems use binary number system to operate. Some common examples of digital systems include digital computers, laptops, smartphones, etc. This chapter is meant for explaining the major components of a digital system. Components of a Digital System A typical digital system consists of the following main components − Central Processing Unit (CPU) Memory Input Devices Output Devices Logic Gates Power Supply Communication Channels Let’s discuss each of these components of a digital system in detail. Central Processing Unit (CPU) In a digital system, the central processing unit is the most important component of the system, as it performs all the operations in the system. It is also known as processor. The CPU is an electronic circuit that consists of two sub-circuits namely, arithmetic and logic unit, and control unit. The arithmetic logic unit (ALU) is the part of a CPU that performs all the arithmetic and logical operations and executes the instructions to manipulate data. ALU is made up of logic gates and other electronic components. It can perform operations like addition, subtractions, comparison, etc. The control unit (CU) is another major electronic circuit in the central processing unit that coordinate the operation of all other components of a digital system. It generates clock signals for the synchronization of the system. Semiconductor Memory Memory is another major component of a digital system. It is used to store and instructions in the system. In most digital system, semiconductor memory is used to store digital information. Memory of a digital system can be classified into the following two types − Random Access Memory (RAM) − It is a temporary memory used to store data and instruction on which the CPU is currently working. Once the digital system is turned off, its data will be deleted. Read Only Memory (ROM) − ROM is also an important component of a digital system. It is a permanent memory used to store those data and instructions that require again and again to perform tasks. In digital systems, both RAM and ROM are used in the form of ICs made up of semiconductors. Apart from RAM and ROM, digital systems may also support external memory devices like CD, DVD, Pen Drive, SD card, etc. All these external memories are used for permanent data storage. Input Devices Input devices are those electronic components of a digital system used for entering data into the system. Examples of input devices include keyboard, mouse, scanner, sensors, camera, light pen, code readers, etc. Input devices are designed to accept data in the form of a specific type or format and convert them into digital signals for processing. For example, a keyboard gets outside instructions in the form of keystrokes and then convert them into digital signals. Output Devices Output devices are those components of a digital system that allow users to view the processed data or information. Examples of output devices are monitor, display screens, printers, projectors, speakers, etc. Output devices are designed to accept digital signals and convert them in a suitable format to make them readable by human. For example, a monitor takes digital signals and convert them as visuals and display on a screen. Logic Gates Logic gates are essential components of any digital system. They are the fundamental building block of the digital system. Logic gates are nothing but electronic circuits that can perform logical operations. In digital systems, logic gates are used to realize all the information processing and storage systems. The most commonly used logic gates are AND, OR, NOT, NAND, NOR, Ex-OR, and Ex-NOR. Power Supply Power supply is the energy bank of the digital system that provides necessary electric power to the components of the system so they can work. The primary function of the power supply unit of a digital system is to convert the electric power received from an external source into the desired type and voltage level required by the system. Most digital systems work on 5 V DC supply. Hence, the power supply unit receives 220 V AC from the supply mains and convert it to 5 V DC supply. Also, the power supply unit regulates the fluctuations occurring in the power supply to protect the system from damages. Communication Channels In a digital system, the communication channel is also known as bus system. It consists of several different types of buses (conductors) such as data bus, address bus, and control bus. These communication channels allow data transmission between different components of the system. Conclusion In conclusion, a digital system consists of several components. Some important components of a typical digital system are described in this chapter. All these components are connected together and allowed to communicate to perform different jobs. In the next chapter, we will learn about different types of “digital logic operations”. Print Page Previous Next Advertisements ”;

Digital Logic Operations ”; Previous Next 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