Basic Logic Gates with Truth Tables discusses the basic logic gates used in digital circuits, including AND, OR, NOT, NAND, NOR, XOR, and XNOR gates. It explains what logic gates are, how they are implemented, and provides truth tables showing the output for all possible combinations of inputs for each gate. The document is intended to provide an overview of basic logic gates and their functions using truth tables.
An encoder is a circuit that takes a digital input and converts it to a binary code output. It performs the inverse operation of a decoder. There are different types of encoders like priority encoders, decimal to binary coded decimal encoders, and hexadecimal to binary encoders. A priority encoder gives priority to certain input lines such that if multiple lines are high, the output corresponds to the highest priority line. A decimal to BCD encoder takes a 10-bit decimal input and produces a 4-bit binary coded decimal output corresponding to each decimal value. Standard encoder integrated circuits like the 74HC147 implement common encoder functions.
Group members for the project are Falah Hassan, Maidah Malik, and Maria Khan. The document discusses half adders and full adders. A half adder adds two binary digits and produces a sum and carry output. It is built from two logic gates. A full adder accepts two input bits and a carry input, and produces a sum and carry output. It is implemented using two half adders joined by an OR gate. The main difference between a half adder and full adder is that a full adder has three inputs and two outputs, allowing multiple adders to be chained to add more bits.
A multiplexer is a digital circuit that has multiple inputs and a single output. It selects one of the multiple input lines to pass to its output based on a digital select line. A multiplexer uses select lines to determine which input is passed to the output. Multiplexers come in different sizes depending on the number of inputs and select lines, such as 2-to-1, 4-to-1, and 8-to-1 multiplexers. Multiplexers are used in applications such as data communications, audio/video routing, and implementing digital logic functions.
This document discusses various logic gates and their truth tables. It begins by explaining the AND, OR, and NOT gates and providing their respective logic symbols, descriptions, and truth tables. It then covers the NAND, NOR, XOR, and XNOR gates. The document also provides an example of converting a logic circuit diagram into a truth table and a Boolean expression. Finally, it discusses implementations of logic gates using integrated circuits and the use of Karnaugh maps to minimize logic expressions.
NAND and NOR gates are universal logic gates because they can be used to implement all other basic logic gates. Specifically:
- A NAND gate can act as an inverter, and two or three NAND gates can be configured to act as an AND gate or OR gate respectively.
- Similarly, a NOR gate can act as an inverter, and two or three NOR gates can be arranged to perform the logic of an OR gate or AND gate.
This property means that only NAND or NOR gates are needed to build any digital circuit, making them universal fundamental building blocks for logic.
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
An encoder is a circuit that takes a digital input and converts it to a binary code output. It performs the inverse operation of a decoder. There are different types of encoders like priority encoders, decimal to binary coded decimal encoders, and hexadecimal to binary encoders. A priority encoder gives priority to certain input lines such that if multiple lines are high, the output corresponds to the highest priority line. A decimal to BCD encoder takes a 10-bit decimal input and produces a 4-bit binary coded decimal output corresponding to each decimal value. Standard encoder integrated circuits like the 74HC147 implement common encoder functions.
Group members for the project are Falah Hassan, Maidah Malik, and Maria Khan. The document discusses half adders and full adders. A half adder adds two binary digits and produces a sum and carry output. It is built from two logic gates. A full adder accepts two input bits and a carry input, and produces a sum and carry output. It is implemented using two half adders joined by an OR gate. The main difference between a half adder and full adder is that a full adder has three inputs and two outputs, allowing multiple adders to be chained to add more bits.
A multiplexer is a digital circuit that has multiple inputs and a single output. It selects one of the multiple input lines to pass to its output based on a digital select line. A multiplexer uses select lines to determine which input is passed to the output. Multiplexers come in different sizes depending on the number of inputs and select lines, such as 2-to-1, 4-to-1, and 8-to-1 multiplexers. Multiplexers are used in applications such as data communications, audio/video routing, and implementing digital logic functions.
This document discusses various logic gates and their truth tables. It begins by explaining the AND, OR, and NOT gates and providing their respective logic symbols, descriptions, and truth tables. It then covers the NAND, NOR, XOR, and XNOR gates. The document also provides an example of converting a logic circuit diagram into a truth table and a Boolean expression. Finally, it discusses implementations of logic gates using integrated circuits and the use of Karnaugh maps to minimize logic expressions.
NAND and NOR gates are universal logic gates because they can be used to implement all other basic logic gates. Specifically:
- A NAND gate can act as an inverter, and two or three NAND gates can be configured to act as an AND gate or OR gate respectively.
- Similarly, a NOR gate can act as an inverter, and two or three NOR gates can be arranged to perform the logic of an OR gate or AND gate.
This property means that only NAND or NOR gates are needed to build any digital circuit, making them universal fundamental building blocks for logic.
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
The document discusses encoders, decoders, multiplexers (MUX), and how they can be used to implement digital logic functions. It provides examples of using 4-to-1, 8-to-1 and 10-to-1 MUX to implement functions. It also gives examples of 4-to-2, 8-to-3 and 10-to-4 encoders. Decoder examples include a 2-to-4 and 3-to-8 binary decoder. The document explains how decoders can be used as logic building blocks to realize Boolean functions. It poses questions to be answered using terms like MUX, DEMUX, encoder, decoder.
This document discusses multiplexers and demultiplexers. It defines them as devices that allow digital information from several sources to be routed onto a single line (multiplexers) or distributed to multiple output lines (demultiplexers). The key properties of multiplexers and demultiplexers are described, including the relationship between the number of inputs, outputs, and selection lines. Examples of implementing multiplexers and demultiplexers using logic gates are provided.
In digital electronics, a decoder can take the form of a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different e.g. n-to-2n , binary-coded decimal decoders. Decoding is necessary in applications such as data multiplexing, 7 segment display and memory address decoding.
An encoder is a device, circuit, transducer, software program, algorithm or person that converts information from one format or code to another. The purpose of encoder is standardization, speed, secrecy, security, or saving space by shrinking size. Encoders are combinational logic circuits and they are exactly opposite of decoders. They accept one or more inputs and generate a multibit output code.
This presentation introduces encoders. It discusses that an encoder is a combinational circuit that performs the reverse operation of a decoder, with a maximum of 2n inputs and n outputs. The simplest encoder is a 2n-to-n binary encoder, where one of the 2n inputs is 1 and the output is an n-bit binary number representing the activated input. An example of an 8-to-3 binary encoder is shown, where only one of the 8 inputs can be activated at a time, and the 3 outputs represent the activated input in binary code.
Dr. Gargi Khanna teaches digital electronics and logic design at the National Institute of Technology in Hamirpur. The document defines digital signals as having two discrete levels (HIGH and LOW), and describes the basic logic gates - NOT, AND, OR, NAND, NOR, XOR, and XNOR. It provides truth tables and Boolean equations for each gate, discusses their implementation using transistors or diodes, and gives examples of applications. Universal gates like NAND and NOR are also covered, along with how to realize other logic functions using them. Integrated circuits for common logic gates are briefly described.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
Synchronous down counter with full description.
All the flip-flop are clocked simultaneously.
Synchronous counters can operate at much higher frequencies than asynchronous counters.
As clock is simultaneously given to all flip-flops there is no problem of propagation delay. Hence they are high speed counters and are preferred when number of flip-flops increase's in the given design.
In this counter will counter
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
This document discusses parity generators and checkers, which are used to detect errors in digital data transmission. It explains that a parity generator adds an extra parity bit to binary data to make the total number of 1s either even or odd. This allows a parity checker circuit at the receiver to detect errors if the number of 1s is the wrong parity. It provides truth tables and logic diagrams for 3-bit even and odd parity generators and an even parity checker. The boolean expressions for the parity generator and checker circuits are also derived.
This document discusses digital logic circuits and binary logic. It begins with an overview of binary logic, logic gates like NAND, NOR and XOR, and Boolean algebra. It then covers analog vs digital signals, quantization, and converting between analog and digital formats. Various representations of digital designs are presented, including truth tables, Boolean algebra, and schematics. Common logic gates and their representations are described. The document discusses design methodologies and analyses, as well as simulation of logic circuits. It also covers elementary binary logic functions, basic identities of Boolean algebra, and converting between Boolean expressions and logic circuits.
Basic theorems and properties of boolean algebraHanu Kavi
The document discusses Boolean algebra laws and theorems that are used to simplify Boolean expressions and logic. Some of the key laws and theorems covered include the associative, distributive, commutative, absorption, and duality laws. De Morgan's theorems are also explained, which relate to taking the complement of a sum or product of variables. Truth tables are used to demonstrate De Morgan's theorems. The overall purpose is to provide some of the fundamental laws and theorems of Boolean algebra that can be applied to simplify logical expressions.
This document summarizes key concepts about combinational logic circuits. It defines combinational logic as circuits whose outputs depend only on the current inputs, in contrast to sequential logic which also depends on prior inputs. Common combinational circuits are described like half and full adders used for arithmetic, as well as decoders. The design process for combinational circuits is outlined involving specification, formulation, optimization and technology mapping. Implementation of functions using NAND and NOR gates is also discussed.
This presentation introduces digital logic gates and their applications. It discusses different types of logic gates like AND, OR, NOT, NAND, NOR gates. It explains how individual logic gates can be connected to form more complex circuits. The presentation also covers topics like different logic gate families (TTL, CMOS), their input/output voltage levels, integrated circuit classification based on transistor count (SSI, MSI, LSI, VLSI etc.) and sources of noise in digital circuits.
A combinational circuit is a logic circuit whose output is solely determined by the present input. It has no internal memory and its output depends only on the current inputs. A half adder is a basic combinational circuit that adds two single bits and produces a sum and carry output. A full adder adds three bits and produces a sum and carry like the half adder. Other combinational circuits discussed include half and full subtractors, decoders, encoders, and priority encoders.
This document summarizes sequential circuits and their basic components - latches and flip-flops. It describes how latches like the SR, S'R', and D latches work based on inputs but no clock signal, while flip-flops like edge-triggered flip-flops change state based on the clock edge. Examples of additional flip-flop inputs like preset, clear and clock enable are provided to control the output independent of the clock. Asynchronous sequential circuits can override the clock input using preset and clear inputs to directly control the output states.
This document discusses counters, which are digital circuits used for counting pulses. It describes asynchronous and synchronous counters, and different types including up/down counters, decade counters, ring counters, and Johnson counters. Examples of counter applications are given such as in kitchen appliances, washing machines, microwaves, and programmable logic controllers. Counters are used for tasks like time measurement, frequency division, and digital signal generation.
The document discusses the basic logic gates used in digital electronics. It defines logic gates as basic building blocks that have one or more inputs and one output, and perform logical operations on binary inputs. The seven basic logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each gate is explained with its truth table that shows the output for every combination of 1s and 0s on the inputs. Logic gates are used as fundamental building blocks in digital circuits and microprocessors to perform logical functions.
M. FLORENCE DAYANA/unit - II logic gates and circuits.pdfDr.Florence Dayana
Logic Gates, Truth Table, AND Gate
Types of Digital Logic AND Gate, The 2-input and 3-input AND Gate, OR Gate, Types of Digital Logic AND Gate, The 2-input OR gate, The 3-input OR gate, NOT Gate, NAND Gate, The 2-input NAND Gate, The 3-input NAND Gate, NOR Gate, 2-input NOR gate
Just like other gates, XOR gate or Exclusive-OR gate
The document discusses encoders, decoders, multiplexers (MUX), and how they can be used to implement digital logic functions. It provides examples of using 4-to-1, 8-to-1 and 10-to-1 MUX to implement functions. It also gives examples of 4-to-2, 8-to-3 and 10-to-4 encoders. Decoder examples include a 2-to-4 and 3-to-8 binary decoder. The document explains how decoders can be used as logic building blocks to realize Boolean functions. It poses questions to be answered using terms like MUX, DEMUX, encoder, decoder.
This document discusses multiplexers and demultiplexers. It defines them as devices that allow digital information from several sources to be routed onto a single line (multiplexers) or distributed to multiple output lines (demultiplexers). The key properties of multiplexers and demultiplexers are described, including the relationship between the number of inputs, outputs, and selection lines. Examples of implementing multiplexers and demultiplexers using logic gates are provided.
In digital electronics, a decoder can take the form of a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different e.g. n-to-2n , binary-coded decimal decoders. Decoding is necessary in applications such as data multiplexing, 7 segment display and memory address decoding.
An encoder is a device, circuit, transducer, software program, algorithm or person that converts information from one format or code to another. The purpose of encoder is standardization, speed, secrecy, security, or saving space by shrinking size. Encoders are combinational logic circuits and they are exactly opposite of decoders. They accept one or more inputs and generate a multibit output code.
This presentation introduces encoders. It discusses that an encoder is a combinational circuit that performs the reverse operation of a decoder, with a maximum of 2n inputs and n outputs. The simplest encoder is a 2n-to-n binary encoder, where one of the 2n inputs is 1 and the output is an n-bit binary number representing the activated input. An example of an 8-to-3 binary encoder is shown, where only one of the 8 inputs can be activated at a time, and the 3 outputs represent the activated input in binary code.
Dr. Gargi Khanna teaches digital electronics and logic design at the National Institute of Technology in Hamirpur. The document defines digital signals as having two discrete levels (HIGH and LOW), and describes the basic logic gates - NOT, AND, OR, NAND, NOR, XOR, and XNOR. It provides truth tables and Boolean equations for each gate, discusses their implementation using transistors or diodes, and gives examples of applications. Universal gates like NAND and NOR are also covered, along with how to realize other logic functions using them. Integrated circuits for common logic gates are briefly described.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
Synchronous down counter with full description.
All the flip-flop are clocked simultaneously.
Synchronous counters can operate at much higher frequencies than asynchronous counters.
As clock is simultaneously given to all flip-flops there is no problem of propagation delay. Hence they are high speed counters and are preferred when number of flip-flops increase's in the given design.
In this counter will counter
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
This document discusses parity generators and checkers, which are used to detect errors in digital data transmission. It explains that a parity generator adds an extra parity bit to binary data to make the total number of 1s either even or odd. This allows a parity checker circuit at the receiver to detect errors if the number of 1s is the wrong parity. It provides truth tables and logic diagrams for 3-bit even and odd parity generators and an even parity checker. The boolean expressions for the parity generator and checker circuits are also derived.
This document discusses digital logic circuits and binary logic. It begins with an overview of binary logic, logic gates like NAND, NOR and XOR, and Boolean algebra. It then covers analog vs digital signals, quantization, and converting between analog and digital formats. Various representations of digital designs are presented, including truth tables, Boolean algebra, and schematics. Common logic gates and their representations are described. The document discusses design methodologies and analyses, as well as simulation of logic circuits. It also covers elementary binary logic functions, basic identities of Boolean algebra, and converting between Boolean expressions and logic circuits.
Basic theorems and properties of boolean algebraHanu Kavi
The document discusses Boolean algebra laws and theorems that are used to simplify Boolean expressions and logic. Some of the key laws and theorems covered include the associative, distributive, commutative, absorption, and duality laws. De Morgan's theorems are also explained, which relate to taking the complement of a sum or product of variables. Truth tables are used to demonstrate De Morgan's theorems. The overall purpose is to provide some of the fundamental laws and theorems of Boolean algebra that can be applied to simplify logical expressions.
This document summarizes key concepts about combinational logic circuits. It defines combinational logic as circuits whose outputs depend only on the current inputs, in contrast to sequential logic which also depends on prior inputs. Common combinational circuits are described like half and full adders used for arithmetic, as well as decoders. The design process for combinational circuits is outlined involving specification, formulation, optimization and technology mapping. Implementation of functions using NAND and NOR gates is also discussed.
This presentation introduces digital logic gates and their applications. It discusses different types of logic gates like AND, OR, NOT, NAND, NOR gates. It explains how individual logic gates can be connected to form more complex circuits. The presentation also covers topics like different logic gate families (TTL, CMOS), their input/output voltage levels, integrated circuit classification based on transistor count (SSI, MSI, LSI, VLSI etc.) and sources of noise in digital circuits.
A combinational circuit is a logic circuit whose output is solely determined by the present input. It has no internal memory and its output depends only on the current inputs. A half adder is a basic combinational circuit that adds two single bits and produces a sum and carry output. A full adder adds three bits and produces a sum and carry like the half adder. Other combinational circuits discussed include half and full subtractors, decoders, encoders, and priority encoders.
This document summarizes sequential circuits and their basic components - latches and flip-flops. It describes how latches like the SR, S'R', and D latches work based on inputs but no clock signal, while flip-flops like edge-triggered flip-flops change state based on the clock edge. Examples of additional flip-flop inputs like preset, clear and clock enable are provided to control the output independent of the clock. Asynchronous sequential circuits can override the clock input using preset and clear inputs to directly control the output states.
This document discusses counters, which are digital circuits used for counting pulses. It describes asynchronous and synchronous counters, and different types including up/down counters, decade counters, ring counters, and Johnson counters. Examples of counter applications are given such as in kitchen appliances, washing machines, microwaves, and programmable logic controllers. Counters are used for tasks like time measurement, frequency division, and digital signal generation.
The document discusses the basic logic gates used in digital electronics. It defines logic gates as basic building blocks that have one or more inputs and one output, and perform logical operations on binary inputs. The seven basic logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Each gate is explained with its truth table that shows the output for every combination of 1s and 0s on the inputs. Logic gates are used as fundamental building blocks in digital circuits and microprocessors to perform logical functions.
M. FLORENCE DAYANA/unit - II logic gates and circuits.pdfDr.Florence Dayana
Logic Gates, Truth Table, AND Gate
Types of Digital Logic AND Gate, The 2-input and 3-input AND Gate, OR Gate, Types of Digital Logic AND Gate, The 2-input OR gate, The 3-input OR gate, NOT Gate, NAND Gate, The 2-input NAND Gate, The 3-input NAND Gate, NOR Gate, 2-input NOR gate
Just like other gates, XOR gate or Exclusive-OR gate
Logic gates are basic electronic circuits that perform logical operations and produce binary outputs. The common logic gates are OR, AND, NOT, NAND, NOR, XOR, and XNOR. An OR gate output is 1 if one or more inputs are 1. An AND gate output is 1 only if all inputs are 1. A NOT gate inverts the input so its output is the opposite state. Combinations of gates can create more complex gates like NAND and NOR. Logic gates have applications in electronic devices like alarms and locks.
1. Digital electronics deals with data and codes represented in a digital format using two conditions: 0 and 1.
2. Digital circuits are made from logic gates, which perform operations on binary inputs to produce binary outputs according to truth tables.
3. Common logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR gates, which can be combined to perform more complex operations.
logic gates ,truth table , boolean expression, basic gates, universal gates . what is and gate , or gate , not gate , nand gate , nor gate , what is logic circuit , symbol of and gate , not gate , or gate
The document introduces basic electronic gates and their functions. It describes that gates require a power supply and have two nominal voltage values representing 0s and 1s. The main gates are AND, OR, NOT, NAND, NOR, EXOR and EXNOR, which are the building blocks for digital systems. Each gate is defined by its truth table, with NAND and NOR being able to represent all other gate functions.
Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic. Based on this, logic gates are named as AND gate, OR gate, NOT gate etc.
The document discusses the fundamentals of digital logic gates. It describes the basic logic gates - NOT, AND, and OR - and how more complex gates like NAND, NOR, XOR, and XNOR are derived from combining these basic gates. It also provides truth tables that define the input and output behavior of each gate. The document explains that logic circuits are built by connecting individual logic gates together and that these circuits have applications in areas like computing, engineering, and automation.
This document provides an overview of digital electronics and electronic principles. It covers topics such as number systems, binary codes, Boolean algebra, logic gates, and applications of digital circuits. Number systems and conversions between binary, decimal, octal, and hexadecimal are examined. Boolean algebra and logic gates like AND, OR, NOT, NAND, and NOR are described along with their truth tables. Combinational logic circuits including adders, multiplexers, and decoders are discussed. Sequential logic and memory elements like latches and flip-flops are also introduced. The document provides fundamental information on digital electronics and serves as an introduction to the key concepts and components in the field.
Digital logic design uses binary numbers (zeros and ones) to create inputs and outputs for electronic devices. As a digital logic designer, you could help develop technologies like cell phones, computers, and other personal electronics. Digital logic is based on binary code and logic gates like AND, OR, NOT, NAND, NOR, and XOR, which can be combined into more complex circuits. This lab experiment aims to verify the truth tables of these basic logic gates by building circuits on a trainer and testing all input combinations to check the output.
Digital systems use logic gates like AND, OR, NOT, NAND, NOR, EXOR and EXNOR. The AND gate outputs 1 only if all inputs are 1. The OR gate outputs 1 if one or more inputs are 1. The NOT gate inverts the input, outputting 1 for a 0 input and vice versa. NAND and NOR gates are composed of an AND/OR gate followed by a NOT. EXOR outputs 1 if either but not both inputs are 1, while EXNOR does the opposite. Truth tables define all possible input/output combinations for each gate.
The document discusses the basics of logic gates and how they can be constructed from transistors. It explains that a NAND gate can be made from two transistors and a resistor. All other logic gates like AND, OR, XOR, NOT can then be constructed by combining NAND gates in different configurations. The document also introduces the common symbols and truth tables used to represent different logic gates. It describes how more complex gates with multiple inputs can be built by combining simpler two-input gates.
This document provides an overview of logic gates. It begins by defining logic gates as the fundamental building blocks of digital electronics that perform logical operations on inputs and produce single outputs. The major types of logic gates - NOT, AND, OR, and XOR - are described. Additional gates like NAND, NOR, and XNOR are also mentioned. Each gate's inputs, outputs, and functions are defined. The document aims to introduce the basic types of logic gates and their uses as building blocks in digital circuits and electronics.
This document defines and explains various logic gates through truth tables and diagrams. It discusses AND, OR, NOT, NAND, NOR, XOR, and XNOR gates. For each gate, it provides the symbol, concept/definition, and a truth table showing the input-output relationships. The document is intended to teach the basic concepts of logic gates and how truth tables are used to represent their functions.
This presentation introduces several types of digital logic gates: AND, OR, NOT, NAND, NOR, and XOR gates. It describes the functionality of each gate, showing how the output is determined based on the input(s). Circuit diagrams and truth tables are provided to illustrate the logic behavior of AND, OR, NOT, NAND, NOR, and XOR gates. The presentation was delivered to the Associate Professor and Associate Head of the Department of Electrical and Electronic Engineering at Daffodil International University by five students.
Digital logic gates are the basic building blocks of digital circuits. The three main types of logic gates are AND gates, OR gates, and NOT gates. Logic gates have one or more inputs and one output, and the output depends on the combinations of inputs according to truth tables. Common logic gates include AND, OR, NAND, NOR, XOR, and XNOR gates. Logic gates can be combined to perform more complex logical operations and form the basis of digital electronics in computers and other devices.
this presentation explains how data is represented in digital computer. it describes digital logic, logic gates and boolean functions. you can learn how to convert boolean function into logic circuit
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Basic Logic Gates with Truth Tables.pdf
1. Basic Logic Gates with Truth Tables
Nowadays, computers have become an integral part of life as they perform many tasks and
operations in quite a short span of time. One of the most important functions of the CPU in
a computer is to perform logical operations by utilizing hardware like Integrated
Circuits software technologies & electronic circuits, But, how this hardware and software
perform such operations is a mysterious puzzle. In order to have a better understanding of
such a complex issue, we must have to acquaint ourselves with the term Boolean Logic,
developed by George Boole. For a simple operation, computers utilize binary digits rather
than digital digits. All the operations are carried out by the Basic Logic gates. This article
discusses an overview of what are basic logic gates in digital electronics and their working.
What are Basic Logic Gates?
A logic gate is a basic building block of a digital circuit that has two inputs and one output.
The relationship between the i/p and the o/p is based on a certain logic. These gates are
implemented using electronic switches like transistors, diodes. But, in practice, basic logic
gates are built using CMOS technology, FETS, and MOSFET(Metal Oxide Semiconductor
FET)s. Logic gates are used in microprocessors, microcontrollers, embedded system
applications, and in electronic and electrical project circuits. The basic logic gates are
categorized into seven: AND, OR, XOR, NAND, NOR, XNOR, and NOT. These logic gates
with their logic gate symbols and truth tables are explained below.
Basic Logic Gates Operation
What are the 7 Basic Logic Gates?
The basic logic gates are classified into seven types: AND gate, OR gate, XOR gate,
NAND gate, NOR gate, XNOR gate, and NOT gate. The truth table is used to show the
logic gate function. All the logic gates have two inputs except the NOT gate, which has
only one input.
When drawing a truth table, the binary values 0 and 1 are used. Every possible
combination depends on the number of inputs. If you don’t know about the logic gates and
their truth tables and need guidance on them, please go through the following infographic
that gives an overview of logic gates with their symbols and truth tables.
Why we use Basic Logic Gates?
The basic logic gates are used to perform fundamental logical functions. These are the
basic building blocks in the digital ICs (integrated circuits). Most of the logic gates use two
binary inputs and generates a single output like 1 or 0. In some electronic circuits, few
2. logic gates are used whereas in some other circuits, microprocessors include millions of
logic gates.
The implementation of Logic gates can be done through diodes, transistors, relays,
molecules, and optics otherwise different mechanical elements. Because of this reason,
basic logic gates are used like electronic circuits.
Binary & Decimal
Before talking about the truth tables of logic gates, it is essential to know the background
of binary & decimal numbers. We all know the decimal numbers which we utilize in
everyday calculations like 0 to 9. This kind of number system includes the base-10. In the
same way, binary numbers like 0 and 1 can be utilized to signify decimal numbers
wherever the base of the binary numbers is 2.
The significance of using binary numbers here is to signify the switching position
otherwise voltage position of a digital component. Here 1 represents the High signal or
high voltage whereas “0” specifies low voltage or low signal. Therefore, Boolean algebra
was started. After that, each logic gate is discussed separately this contains the logic of
the gate, truth table, and its typical symbol.
Types of Logic Gates
The different types of logic gates and symbols with truth tables are discussed below.
Basic Logic Gates
AND Gate
The AND gate is a digital logic gate with ‘n’ i/ps one o/p, which performs logical conjunction
based on the combinations of its inputs. The output of this gate is true only when all the
inputs are true. When one or more inputs of the AND gate’s i/ps are false, then only the
output of the AND gate is false. The symbol and truth table of an AND gate with two inputs
is shown below.
3. AND Gate and its Truth Table
OR Gate
The OR gate is a digital logic gate with ‘n’ i/ps and one o/p, that performs logical conjunction
based on the combinations of its inputs. The output of the OR gate is true only when one or
more inputs are true. If all the i/ps of the gate are false, then only the output of the OR gate
is false. The symbol and truth table of an OR gate with two inputs is shown below.
OR Gate and its Truth Table
NOT Gate
The NOT gate is a digital logic gate with one input and one output that operates an inverter
operation of the input. The output of the NOT gate is the reverse of the input. When the
input of the NOT gate is true then the output will be false and vice versa. The symbol and
truth table of a NOT gate with one input is shown below. By using this gate, we can
implement NOR and NAND gates
NOT Gate and Its Truth Table
NAND Gate
The NAND gate is a digital logic gate with ‘n’ i/ps and one o/p, that performs the operation
of the AND gate followed by the operation of the NOT gate.NAND gate is designed by
combining the AND and NOT gates. If the input of the NAND gate high, then the output of
the gate will be low.The symbol and truth table of the NAND gate with two inputs is shown
below.
4. NAND Gate and its Truth Table
NOR Gate
The NOR gate is a digital logic gate with n inputs and one output, that performs the operation
of the OR gate followed by the NOT gate. NOR gate is designed by combining the OR and
NOT gate. When any one of the i/ps of the NOR gate is true, then the output of the NOR
gate will be false. The symbol and truth table of the NOR gate with the truth table is shown
below.
NOR Gate and Its Truth Table
Exclusive-OR Gate
The Exclusive-OR gate is a digital logic gate with two inputs and one output. The short form
of this gate is Ex-OR. It performs based on the operation of the OR gate. . If any one of the
inputs of this gate is high, then the output of the EX-OR gate will be high. The symbol and
truth table of the EX-OR are shown below.
EX-OR gate and Its Truth Table
Exclusive-NOR Gate
The Exclusive-NOR gate is a digital logic gate with two inputs and one output. The short
form of this gate is Ex-NOR. It performs based on the operation of the NOR gate. When
both the inputs of this gate are high, then the output of the EX-NOR gate will be high. But,
if any one of the inputs is high (but not both), then the output will be low. The symbol and
truth table of the EX-NOR are shown below.
5. EX-NOR Gate and Its Truth Table
The applications of logic gates are mainly determined based upon their truth table, i.e., their
mode of operations. The basic logic gates are used in many circuits like a push-button lock,
light-activated burglar alarm, safety thermostat, an automatic watering system, etc.
Truth Table to Express Logic Gate Circuit
Gate circuit can be expressed using a common method is known as a truth table. This
table includes all the input logic state combinations either high (1) or low (0) for every input
terminal of the logic gate through the equivalent output logic level like high or low. The
NOT logic gate circuit is shown above and its truth table is extremely easy indeed
The truth tables of logic gates are very complex but larger than the NOT gate. The truth
table of each gate must include many rows like there are possibilities for exclusive
combinations for inputs. For instance, for the NOT gate, there are two possibilities of
inputs either 0 or 1, whereas, for the two-input logic gate, there are four possibilities like
00, 01, 10 & 11. Therefore, it includes four rows for the equivalent truth table.
For a 3-input logic gate, there are 8 possible inputs like 000, 001, 010, 011, 100, 101, 110
& 111. Therefore, a truth table including 8 rows is required. Mathematically, the required
number of rows in the truth table is equivalent to 2 increased to the power of the no. of i/p
terminals.
Analysis
The voltage signals in the digital circuits are represented with binary values like 0’s & 1’s
calculated in reference to ground. The deficiency of voltage mainly signifies a “0” whereas
the existence of full DC supply voltage signifies a “1”.
A logic gate is a special type of amplifier circuit that is mainly designed for input as well as
output logic level voltages. Logic gate circuits are most frequently symbolized with a
schematic diagram through their own exclusive symbols Instead of their essential resistors
and transistors.
Just like with Op-Amps (operational amplifiers), the connections of power supply to logic
gates are frequently misplaced in schematic diagrams for the benefit of simplicity. It
includes the probable input logic level combinations through their particular output logic
levels.
6. What is the Easiest Way to Learn Logic Gates?
The easiest way to learn the function of basic logic gates is explained below.
• For AND Gate – If both the inputs are high then the output is also high
• For OR Gate – If a minimum of one input is high then the output is High
• For XOR Gate – If the minimum one input is high then only the output is high
• NAND Gate – If the minimum one input is low then the output is high
• NOR Gate – If both the inputs are low then the output is high.
De Morgan’s Theorem
The first theorem of DeMorgan states that the logic gate like NAND is equal to an OR gate
with a bubble. The logic function of the NAND gate is
A’B = A’+B’
The second theorem of DeMorgan states that the NOR logic gate is equal to an AND gate
with a bubble. The logic function of NOR gate is
(A+B)’= A’. B’
The Conversion of NAND Gate
The NAND gate can be formed using AND gate & NOT gate. The Boolean expression &
truth table is shown below.
NAND Logic Gates Formation
Y= (A⋅B)’
A
B Y′=A⋅ B
Y
0
0 0 1
0
1 0 1
1 0 0
1
1 1 1
0
7. NOR Gate Conversion
The NOR gate can be formed using OR gate & NOT gate. The Boolean expression & truth
table is shown below.
NOR Logic Gates Formation
Y = (A+B)’
A
B Y′ = A+B Y
0
0 0 1
0 1 1
0
1 0 1
0
1 1 1
0
Ex-OR Gate Conversion
The Ex-OR gate can be formed using NOT, AND & OR gate. The Boolean expression &
truth table is shown below. This logic gate can be defined as the gate that gives high
output once any input of this is high. If both the inputs of this gate are high then the output
will be low.
Ex-OR Logic Gates Formation
Y=A⊕Bor A’B+AB’
A B
Y
8. 0
0 0
0
1
1
1 0
1
1 1
0
Ex-NOR Gate Conversion
The Ex-NOR gate can be formed using EX-OR gate & NOT gate. The Boolean expression
& truth table is shown below. In this logic gate, when the output is high “1” then both the
inputs will be either “0” or “1”.
Ex-NOR Gate Formation
Y = (A’B + AB’)’
A
B
Y
0
0 1
0
1 0
1 0
0
1 1
1
Basic Logic Gates using Universal Gates
Universal gates like NAND gate and NOR gate can be implemented through any boolean
expression without using any other type of logic gate. And, they can also be used for
designing any basic logic gate. Additionally, these are extensively utilized in integrated
circuits as they are simple as well as cost-effective to make. The basic logic gates design
using universal gates are discussed below.
The basic logic gates can be designed with the help of universal gates. It uses an error, a
bit of test otherwise you can utilize Boolean logic for attaining these through the logic
9. gates equations for a NAND gate as well as a NOR gate. Here, Boolean logic is used to
solve the output you require. It takes some time but it is needed to perform this to obtain a
hang of Boolean logic as well as basic logic gates.
Basic Logic Gates Using NAND Gate
The designing of basic logic gates using NAND gate is discussed below.
NOT Gate Design using NAND
The designing of the NOT gate is very simple by simply connecting both the inputs as one.
AND Gate Design using NAND
The designing of AND gate using NAND gate can be done at the NAND gate’s output to
reverse it & obtain AND logic.
OR Gate Design using NAND
The designing of OR gate using NAND gate can be done by connecting two NOT gates
using NAND gates at the NAND’s inputs to obtain OR logic.
NOR Gate Design using NAND
The designing of NOR gate using NAND gate can be done by simply connecting another
NOT gate through NAND gate to the o/p of an OR gate through NAND.
EXOR Gate Design using NAND
This one’s a bit tricky. You share the two inputs with three gates. The output of the first
NAND is the second input to the other two. Finally, another NAND takes the outputs of
these two NAND gates to give the final output.
Basic Logic Gates using NOR Gate
The designing of basic logic gates using NOR gate is discussed below.
NOT Gate using NOR
The designing of NOT gate with NOR gate is simple by connecting both the inputs as one.
OR Gate using NOR
The designing of OR Gate with NOR gate is simple by connecting at the o/p of the NOR
gate to reverse it & obtain OR logic.
AND Gate using NOR
The designing of AND gate using NOR gate can be done by connecting two NOT with
NOR gates at the NOR inputs to obtain AND logic.
NAND Gate using NOR
The designing of NAND Gate using NOR gate can be done by simply connecting another
NOT gate through NOR gate to the AND gate’s output with NOR.
10. EX-NOR Gate using NOR
This type of connection is a bit difficult because the two inputs can be shared with three
logic gates. The first NOR gate output is the next input to the remaining two gates. Finally,
another NOR gate uses the two NOR gate outputs to provide the last output.
Applications
The applications of basic logic gates are so many however they mostly depend on their
truth tables otherwise form of operations. Basic logic gates are frequently used in circuits
like a lock with push-button, the watering system automatically, burglar alarm activated
through light, safety thermostat & other types of electronic devices.
The main advantage of basic logic gates is, these can be used in a different combination
circuit. In addition, there is no boundary to the number of logic gates that can be utilized in
a single electronic device. But, it can be limited because of the specified physical gap
within the device. In digital ICs (integrated circuits) we will discover a collection of the logic
gate region unit.
By using mixtures of basic logic gates, advanced operations are often performed. In theory,
there’s no limit to the number of gates that may be clad along during a single device.
However, in the application, there’s a limit to the number of gates that may be packed into
a given physical area. Arrays of the logic gate area unit are found in digital integrated circuits
(ICs). As IC technology advances, the desired physical volume for every individual gate
decreases, and digital devices of an equivalent or smaller size become capable of acting
with more complicated operations at ever-increasing speeds.
This is all about an overview of what is a basic logic gate, types like AND gate, OR gate,
NAND gate, NOR gate, EX-OR gate, and EX-NOR gate. In this, AND, NOT and OR gates
are the basic logic gates. By using these gates we can create any logic gate by combining
them. Where NAND and NOR gates are called universal gates. These gates have a
particular property with which they can create any logical Boolean expression if designed in
a proper way.
Infographics of Logic Gates