This document provides an overview of logic gates, including:
- The main types of logic gates (NOT, AND, NAND, OR, NOR, EX-OR, EX-NOR)
- Their symbols and truth tables
- How logic gates can be combined to perform more complex logic functions
- How different gate types can be substituted using only NAND or NOR gates
The document describes various digital logic gates and their functions. It begins by defining a logic AND gate, which outputs a 1 only when all inputs are 1. It then discusses 2-input and 3-input AND gate symbols and truth tables. Similarly, it defines logic OR, NOT, NAND, NOR, and exclusive-OR gates with their symbols and functions. The document also covers flip-flops, describing an SR flip-flop built from two cross-coupled NAND gates that can store a single bit.
Logic gates are used to represent binary operations. The main logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Truth tables define the output of each gate based on all possible combinations of its inputs. A circuit diagram can be translated to a truth table by considering the output for each input combination.
EASA Part 66 Module 5.5 : Logic Circuitsoulstalker
Presentation slide basic information
AND + OR + NAND + NOR + EX NOR + Application
Other EASA Part66 slide and note can be found here :
http://part66.blogspot.com
The document provides an overview of the digital logic NOT gate:
- It is a single input gate that inverts its input signal, outputting a 0 when the input is 1 and vice versa.
- NOT gates can be constructed using transistors or with NAND and NOR gates connected in a specific configuration.
- The symbol for a NOT gate is a triangle pointing right with a circle "inversion bubble" at the output.
- Common integrated circuit implementations of NOT gates include the 7404 and CD4009.
This document describes several types of logic gates. It defines the NOT, AND, OR, NAND, NOR, XOR, and XNOR gates and provides their truth tables. The key points are:
- Logic gates perform basic Boolean logic operations on binary inputs and produce binary outputs.
- The NOT gate inverts its input. The AND gate outputs 1 only if all inputs are 1. The OR gate outputs 1 if any input is 1.
- The NAND and NOR gates are similar to AND and OR but produce the opposite output. XOR outputs 1 only if inputs differ. XNOR outputs 1 only if inputs are the same.
- Examples of input/output waveforms are provided to illustrate the behavior
This is the project that describes each logic gate briefly. This includes AND , OR, NOT, NOR, NAND,XOR. Each gate has the symbol, working, boolean formula and the observation table.
this project requires breadboard, single stranded wire, battery pack(d.c.) , multimeter and finally their applications.
Rithu
AECS Kudankulam
Logic gates are basic building blocks of digital circuits that control information flow and perform logical operations. The main logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. NAND and NOR gates are considered universal gates as they can be used to implement all other gate functions. Logic gates are represented by symbols and their operations defined by truth tables.
The document describes various digital logic gates and their functions. It begins by defining a logic AND gate, which outputs a 1 only when all inputs are 1. It then discusses 2-input and 3-input AND gate symbols and truth tables. Similarly, it defines logic OR, NOT, NAND, NOR, and exclusive-OR gates with their symbols and functions. The document also covers flip-flops, describing an SR flip-flop built from two cross-coupled NAND gates that can store a single bit.
Logic gates are used to represent binary operations. The main logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Truth tables define the output of each gate based on all possible combinations of its inputs. A circuit diagram can be translated to a truth table by considering the output for each input combination.
EASA Part 66 Module 5.5 : Logic Circuitsoulstalker
Presentation slide basic information
AND + OR + NAND + NOR + EX NOR + Application
Other EASA Part66 slide and note can be found here :
http://part66.blogspot.com
The document provides an overview of the digital logic NOT gate:
- It is a single input gate that inverts its input signal, outputting a 0 when the input is 1 and vice versa.
- NOT gates can be constructed using transistors or with NAND and NOR gates connected in a specific configuration.
- The symbol for a NOT gate is a triangle pointing right with a circle "inversion bubble" at the output.
- Common integrated circuit implementations of NOT gates include the 7404 and CD4009.
This document describes several types of logic gates. It defines the NOT, AND, OR, NAND, NOR, XOR, and XNOR gates and provides their truth tables. The key points are:
- Logic gates perform basic Boolean logic operations on binary inputs and produce binary outputs.
- The NOT gate inverts its input. The AND gate outputs 1 only if all inputs are 1. The OR gate outputs 1 if any input is 1.
- The NAND and NOR gates are similar to AND and OR but produce the opposite output. XOR outputs 1 only if inputs differ. XNOR outputs 1 only if inputs are the same.
- Examples of input/output waveforms are provided to illustrate the behavior
This is the project that describes each logic gate briefly. This includes AND , OR, NOT, NOR, NAND,XOR. Each gate has the symbol, working, boolean formula and the observation table.
this project requires breadboard, single stranded wire, battery pack(d.c.) , multimeter and finally their applications.
Rithu
AECS Kudankulam
Logic gates are basic building blocks of digital circuits that control information flow and perform logical operations. The main logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. NAND and NOR gates are considered universal gates as they can be used to implement all other gate functions. Logic gates are represented by symbols and their operations defined by truth tables.
Logic Gates & Related Device. This contains some basic fundamentals about Logic Gates. I hope, this will be helpful to those interested in Digital Electronics.
This document provides an introduction to basic logic gates. It includes:
1. An introduction that defines logic gates and their use of diodes to allow or block signals based on logic conditions.
2. Descriptions of three basic logic gates - OR, AND, and NOT - including their symbols, Boolean expressions, and truth tables.
3. Sections on each of the three basic gates that explain how to simulate them using components like diodes, transistors, and resistors, and provide examples of their truth tables.
The document serves as an overview of logic gates, their components, representations, and functions as basic building blocks of digital circuits.
The document introduces several basic logic gates - AND, OR, NOT, NAND, and NOR. It describes what each gate is, provides its symbol, and shows its truth table that defines the output for all possible input combinations. The AND gate outputs 1 only if all inputs are 1, while the OR gate outputs 1 if any input is 1. The NOT gate inverts the single input. NAND and NOR gates are combinations of NOT and AND or OR gates respectively, producing the complemented output.
Digital Logic & Computer Architecture Practical Book by Yasir Ahmed KhanYasir Khan
Here are the circuit designs and truth tables for the given Boolean expressions:
1. F = (a.b) (b'+c)
Circuit:
[CIRCUIT DIAGRAM OF GIVEN BOOLEAN EXPRESSION]
Truth Table:
[TRUTH TABLE OF GIVEN BOOLEAN EXPRESSION]
2. F = a + b'c
Circuit:
[CIRCUIT DIAGRAM OF GIVEN BOOLEAN EXPRESSION]
Truth Table:
[TRUTH TABLE OF GIVEN BOOLEAN EXPRESSION]
Please let me know if you need any clarification or have additional questions!
This document describes Virat Prasad's class project to design and simulate logic gate circuits. It includes an introduction to logic gates, descriptions of common logic gates like OR, AND, NOT, NOR and NAND gates. Truth tables and circuit diagrams are provided to explain the working of each gate. The document also acknowledges those who helped with the project and provided a bibliography.
This document provides information about logic gates. It discusses the history of logic gates and binary systems. It then defines common logic gates like OR, AND, NOT, NAND, and NOR gates. For each gate, it provides the symbolic representation, truth table, and examples of how the gate works. It also discusses applications of each gate type in contexts like industrial plants, microwave ovens, car safety systems, freezers, and home security systems. The document is authored by six group members and contains detailed information about the key concepts and components of logic gates.
Circuits are designed using logic gates to control the flow of electronic signals, with basic gates including NOT, AND, OR, and XOR gates. More complex circuits can be created by combining logic gates, such as half and full adders used to perform binary addition. Specialized circuits are designed using a process of identifying inputs/outputs, determining necessary logic gates, constructing truth tables, and evaluating circuit design.
This document discusses logic gates, which are basic building blocks of digital circuits. It defines logic gates as circuits that output a 1 or 0 based on their inputs. The main types of logic gates covered are AND, OR, NOT, NAND, and NOR gates. Their symbols and functions are explained, such as how AND gates output 1 only if all inputs are 1, and OR gates output 1 if any input is 1. Examples of logic gates in daily life are also mentioned.
The document provides details about demonstration experiments involving logic gates and transformers.
It describes the basic logic gates - OR, AND, NOT, NOR, NAND, EXOR and EXNOR - and provides their truth tables and circuit designs. It also explains the working of step-down and step-up transformers through circuit diagrams and discusses transformer ratio, efficiency and various energy losses in transformers.
The document describes various logic gates - AND, OR, NOT, NAND, and NOR gates. It provides the truth tables and Boolean expressions for each gate. It also gives examples of how to derive a truth table from a given logic circuit diagram. NAND and NOR gates are shown to function as inverters in some configurations. The document aims to explain the basic concepts and functions of common logic gates.
verification of logic gates cbse class 12Kirthi Kirthu
This document describes a physics investigatory project on logic gates submitted by S. Kiruthiga of Kendriya Vidyalaya, Dharmapuri. It includes an introduction to logic gates, their basic principles and types including OR, AND, NOT, NOR and NAND gates. Circuit diagrams and truth tables are provided for each gate. The project was guided by [name removed] and certifies this as Kiruthiga's bona fide work.
physics investigatory project class 12 on logic gates ,boolean algebrasukhtej
The document discusses logic gates and their applications. It begins by defining logic gates and their basic components. It then provides details on designing and simulating various logic gate circuits including OR, AND, NOT, NOR, NAND, XOR, XNOR gates. Finally, it discusses some common applications of logic gates such as using OR gates to detect events, AND gates as enable/inhibit gates, XOR/XNOR gates for parity generation/checking, and NOT gates as inverters in oscillators.
Boolean algebra is a logical system used to simplify binary expressions. It uses binary variables that can have a value of 1 or 0, and logical operators like AND, OR and NOT. Boolean expressions can be represented in truth tables and minimized using Karnaugh maps or algebraic manipulation. Key concepts include minterms, maxterms, sum of products form, and product of sums form. Boolean algebra provides a standard way to simplify logical statements and circuits into their essential components.
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
Logic gates are the basic building blocks of digital circuits and perform logical operations. The main logic gates are AND, OR, and NOT. An AND gate outputs 1 only if all its inputs are 1. An OR gate outputs 1 if any of its inputs are 1. A NOT gate inverts its single input. Logic gates are constructed from diodes, transistors, and resistors on a silicon chip and their inputs and outputs represent either 1 or 0, true or false. Combination gates like NAND and NOR are derived from basic logic gates and their truth tables define the output for all possible input combinations.
The document describes several basic logic gates - AND, OR, NOT, NAND, NOR, XOR, and XNOR - and how they operate on binary inputs and outputs. Each gate is defined by a truth table showing the output for all combinations of 0s and 1s on the input lines. Boolean algebra is also mentioned as relating to the logic of these basic digital logic gates.
The document discusses different logic gate implementations using NAND and NOR gates. It explains that AND, OR and NOT functions can be represented as equivalent NAND and NOR logic diagrams. It provides examples of how NAND and NOR gates can be used to implement SUM-OF-PRODUCTS logic functions. Specifically, it shows how a NAND gate implementation can be easily converted to a sum-of-products form using De Morgan's theorem. It also discusses NOR gate implementations and how NOR-NAND and NAND-AND forms are equivalent and can perform AND-OR-INVERT functions.
Logic Gates & Related Device. This contains some basic fundamentals about Logic Gates. I hope, this will be helpful to those interested in Digital Electronics.
This document provides an introduction to basic logic gates. It includes:
1. An introduction that defines logic gates and their use of diodes to allow or block signals based on logic conditions.
2. Descriptions of three basic logic gates - OR, AND, and NOT - including their symbols, Boolean expressions, and truth tables.
3. Sections on each of the three basic gates that explain how to simulate them using components like diodes, transistors, and resistors, and provide examples of their truth tables.
The document serves as an overview of logic gates, their components, representations, and functions as basic building blocks of digital circuits.
The document introduces several basic logic gates - AND, OR, NOT, NAND, and NOR. It describes what each gate is, provides its symbol, and shows its truth table that defines the output for all possible input combinations. The AND gate outputs 1 only if all inputs are 1, while the OR gate outputs 1 if any input is 1. The NOT gate inverts the single input. NAND and NOR gates are combinations of NOT and AND or OR gates respectively, producing the complemented output.
Digital Logic & Computer Architecture Practical Book by Yasir Ahmed KhanYasir Khan
Here are the circuit designs and truth tables for the given Boolean expressions:
1. F = (a.b) (b'+c)
Circuit:
[CIRCUIT DIAGRAM OF GIVEN BOOLEAN EXPRESSION]
Truth Table:
[TRUTH TABLE OF GIVEN BOOLEAN EXPRESSION]
2. F = a + b'c
Circuit:
[CIRCUIT DIAGRAM OF GIVEN BOOLEAN EXPRESSION]
Truth Table:
[TRUTH TABLE OF GIVEN BOOLEAN EXPRESSION]
Please let me know if you need any clarification or have additional questions!
This document describes Virat Prasad's class project to design and simulate logic gate circuits. It includes an introduction to logic gates, descriptions of common logic gates like OR, AND, NOT, NOR and NAND gates. Truth tables and circuit diagrams are provided to explain the working of each gate. The document also acknowledges those who helped with the project and provided a bibliography.
This document provides information about logic gates. It discusses the history of logic gates and binary systems. It then defines common logic gates like OR, AND, NOT, NAND, and NOR gates. For each gate, it provides the symbolic representation, truth table, and examples of how the gate works. It also discusses applications of each gate type in contexts like industrial plants, microwave ovens, car safety systems, freezers, and home security systems. The document is authored by six group members and contains detailed information about the key concepts and components of logic gates.
Circuits are designed using logic gates to control the flow of electronic signals, with basic gates including NOT, AND, OR, and XOR gates. More complex circuits can be created by combining logic gates, such as half and full adders used to perform binary addition. Specialized circuits are designed using a process of identifying inputs/outputs, determining necessary logic gates, constructing truth tables, and evaluating circuit design.
This document discusses logic gates, which are basic building blocks of digital circuits. It defines logic gates as circuits that output a 1 or 0 based on their inputs. The main types of logic gates covered are AND, OR, NOT, NAND, and NOR gates. Their symbols and functions are explained, such as how AND gates output 1 only if all inputs are 1, and OR gates output 1 if any input is 1. Examples of logic gates in daily life are also mentioned.
The document provides details about demonstration experiments involving logic gates and transformers.
It describes the basic logic gates - OR, AND, NOT, NOR, NAND, EXOR and EXNOR - and provides their truth tables and circuit designs. It also explains the working of step-down and step-up transformers through circuit diagrams and discusses transformer ratio, efficiency and various energy losses in transformers.
The document describes various logic gates - AND, OR, NOT, NAND, and NOR gates. It provides the truth tables and Boolean expressions for each gate. It also gives examples of how to derive a truth table from a given logic circuit diagram. NAND and NOR gates are shown to function as inverters in some configurations. The document aims to explain the basic concepts and functions of common logic gates.
verification of logic gates cbse class 12Kirthi Kirthu
This document describes a physics investigatory project on logic gates submitted by S. Kiruthiga of Kendriya Vidyalaya, Dharmapuri. It includes an introduction to logic gates, their basic principles and types including OR, AND, NOT, NOR and NAND gates. Circuit diagrams and truth tables are provided for each gate. The project was guided by [name removed] and certifies this as Kiruthiga's bona fide work.
physics investigatory project class 12 on logic gates ,boolean algebrasukhtej
The document discusses logic gates and their applications. It begins by defining logic gates and their basic components. It then provides details on designing and simulating various logic gate circuits including OR, AND, NOT, NOR, NAND, XOR, XNOR gates. Finally, it discusses some common applications of logic gates such as using OR gates to detect events, AND gates as enable/inhibit gates, XOR/XNOR gates for parity generation/checking, and NOT gates as inverters in oscillators.
Boolean algebra is a logical system used to simplify binary expressions. It uses binary variables that can have a value of 1 or 0, and logical operators like AND, OR and NOT. Boolean expressions can be represented in truth tables and minimized using Karnaugh maps or algebraic manipulation. Key concepts include minterms, maxterms, sum of products form, and product of sums form. Boolean algebra provides a standard way to simplify logical statements and circuits into their essential components.
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
Logic gates are the basic building blocks of digital circuits and perform logical operations. The main logic gates are AND, OR, and NOT. An AND gate outputs 1 only if all its inputs are 1. An OR gate outputs 1 if any of its inputs are 1. A NOT gate inverts its single input. Logic gates are constructed from diodes, transistors, and resistors on a silicon chip and their inputs and outputs represent either 1 or 0, true or false. Combination gates like NAND and NOR are derived from basic logic gates and their truth tables define the output for all possible input combinations.
The document describes several basic logic gates - AND, OR, NOT, NAND, NOR, XOR, and XNOR - and how they operate on binary inputs and outputs. Each gate is defined by a truth table showing the output for all combinations of 0s and 1s on the input lines. Boolean algebra is also mentioned as relating to the logic of these basic digital logic gates.
The document discusses different logic gate implementations using NAND and NOR gates. It explains that AND, OR and NOT functions can be represented as equivalent NAND and NOR logic diagrams. It provides examples of how NAND and NOR gates can be used to implement SUM-OF-PRODUCTS logic functions. Specifically, it shows how a NAND gate implementation can be easily converted to a sum-of-products form using De Morgan's theorem. It also discusses NOR gate implementations and how NOR-NAND and NAND-AND forms are equivalent and can perform AND-OR-INVERT functions.
This document describes the NAND gate, a digital logic gate that implements the NAND logical operation. It has two or more inputs but only one output. The output is HIGH only if at least one of the inputs is LOW, and is LOW only when all inputs are HIGH. NAND gates can be used to implement any Boolean function, and are commonly used to build circuits because they are simple and fast. The document explains how NAND gates can function as NOT, AND, and OR gates and illustrates their pin diagrams and truth tables.
The document summarizes basic digital logic gates and components including NOT, AND, OR, NAND, NOR, XOR, XNOR gates. It also discusses multiplexers, demultiplexers, half/full adders, half/full subtractors, encoders, decoders, and conversions between binary and gray codes.
The document discusses logic gates and their usage. It introduces different logic gates including AND, OR, NAND, NOR, XOR and XNOR. It describes how to draw logic circuits from Boolean expressions and analyze circuits to obtain logical expressions. The document also discusses how NAND and NOR gates are universal and can be used to build any other logic gate. It covers positive and negative logic and how to construct sum-of-product and product-of-sum expressions using logic gates.
The document discusses logic gates and their circuitry. It describes the 7 main logic gates: NOT, AND, OR, NAND, NOR, XOR, and XNOR. It explains how each gate functions and provides their truth tables. The document then details an experiment where samples of each logic gate integrated circuit were connected in a circuit. The output of each gate was tested with different inputs and compared to their truth tables. It aims to help students understand the components and functionality of logic gates.
This document provides an overview of logic gates and digital logic circuits. It defines common logic gates like AND, OR, NOT, NAND and NOR. It describes transistor-transistor logic (TTL) and complementary metal-oxide-semiconductor (CMOS) logic families and their characteristics. Examples of logic circuits using TTL and CMOS gates are also presented.
The document discusses NAND gates and their ability to act as universal logic gates. It defines logic gates and universal logic gates. It then explains that a NAND gate produces an output that is false only if all its inputs are true, which is the complement of an AND gate. The document shows how NAND gates can be used to create NOT, AND and OR gates, demonstrating that all basic logic gates can be made using only NAND gates, giving it the title of universal gate.
This document appears to be a student project report on investigating the relationship between input/output voltage and number of turns in the primary and secondary coils of a transformer. It includes sections on introduction, theory, apparatus, procedure, observations, conclusion, and bibliography. The key points are that the output voltage of a transformer depends on the ratio of turns in the secondary coil to the primary coil, and that there are losses between the input and output resulting in the transformer's efficiency being less than 100%.
The document discusses fault tolerant and online testability in reversible logic synthesis. It proposes a design for a fault tolerant full adder circuit using reversible logic that is both fault tolerant and online testable. The proposed design uses only 3x3 fault tolerant gates, has a minimum number of garbage outputs of 3, and has lower quantum cost compared to an existing design. Performance analysis shows the proposed design has advantages over the existing design in terms of number of gates, garbage outputs, and quantum cost.
Digital logic gates and Boolean algebraSARITHA REDDY
The document discusses digital logic gates and Boolean algebra. It defines logic gates as electronic circuits that make logic decisions. Common logic gates include OR, AND, and NOT gates. Boolean algebra uses truth values of 0 and 1 instead of numbers, and has fundamental laws and operations for AND, OR, and NOT. Boolean algebra can be used to simplify logical expressions and save gates in digital circuit design.
This document provides instructions for laboratory exercises involving digital logic circuits. The exercises include:
1) Studying the operation of logic gates like AND, OR, NOT, NAND, and XOR using integrated circuits and completing truth tables.
2) Verifying Boolean logic laws such as associativity and distributivity using logic gate circuits.
3) Implementing NOT, NAND, NOR, and XOR gates using integrated circuits and observing their truth tables.
4) Demonstrating De Morgan's theorem by connecting logic gate circuits in a specific configuration and completing a truth table.
This document discusses digital logic gates. It begins by defining a gate as a digital circuit with one or more inputs and one output. The three basic gates are described as the NOT, OR, and AND gates. Additional universal gates, the NAND and NOR gates, are introduced. Truth tables are provided to explain the output of each gate for all possible input combinations. The document also discusses how to derive different gate functions using NAND and NOR gates alone through De Morgan's theorems.
Logic gates are basic digital circuits that are used to perform logical operations. The document discusses the common logic gates - AND, OR, NOT, NAND, NOR, XOR and XNOR. It explains their truth tables and symbols. Universal gates like NAND and NOR are able to represent any logical function. Logic gates are the basic building blocks used in digital circuits to perform operations on binary numbers.
Logic gates are electronic circuits that combine multiple inputs to produce an output. There are several types of logic gates that process inputs differently, including AND, OR, NOT, NAND, NOR, XOR, and XNOR gates. Each gate is characterized by its symbol, truth table that specifies the output for every combination of inputs, and Boolean expression that defines its function.
- The document describes several types of basic logic gates - inverter, AND, OR, NAND, NOR, XOR, and XNOR.
- Each logic gate is defined by its truth table and logical expression showing the output for all combinations of inputs.
- Complex logic gates can be constructed by combining simpler gates, such as using two-input AND gates to create a three-input AND gate.
This document discusses different types of logic gates, including their definitions, truth tables, and circuit implementations. It covers basic gates like AND, OR, and NOT; universal gates like NAND and NOR; exclusive gates like XOR and XNOR. It also discusses how logic gates can be implemented using transistors, diodes, and CMOS circuits. Finally, it outlines some common applications of logic gates in areas like microcontrollers, calculators, and digital communications.
1. The document discusses programming for programmable logic controllers (PLCs), including basic PLC operations using binary numbers, logic gates, ladder diagrams, and mnemonic codes.
2. It describes the basic logic functions of AND, OR, and NOT gates that digital devices use, and how ladder diagrams represent circuit diagrams using these logic symbols.
3. The steps for designing ladder diagrams from truth tables or state diagrams are outlined, including converting the diagrams to mnemonic codes that can be programmed into a PLC.
The document discusses different types of logic gates - inverter, AND, OR, NAND, NOR, and exclusive OR (XOR) gates. It provides the truth tables, logic symbols, and logical expressions for each gate. The inverter inverts the input, while AND and NAND gates output 1 only when all inputs are 1. OR and NOR gates output 0 only when all inputs are 0. XOR outputs 1 when only one input is 1, while exclusive NOR (XNOR) outputs 1 when both inputs are the same.
1) Logic gates like AND, OR, NOT, NAND, and NOR are basic digital circuits that perform logical operations on binary inputs and produce binary outputs. Their behavior is defined by truth tables.
2) AND gates output 1 only when all inputs are 1. OR gates output 1 if any input is 1. NAND and NOR gates are universal gates that can be used to implement all other logic functions.
3) Computers use binary number systems like decimal to represent data as strings of 0s and 1s. Decimal uses 10 digits while the position of each digit determines its value and meaning in base-10 numbers.
This document discusses digital circuits and logic gates. It begins with an introduction to analog and digital signals and the binary number system. It then covers Boolean algebra and how it is used to analyze logic gates. The three fundamental logic gates - OR, AND, and NOT - are explained through their truth tables and circuit implementations. More complex gates such as NOR, NAND, and XOR are also introduced and shown to be compositions of the fundamental gates. The document provides detailed explanations of each logic gate's symbol, truth table, and circuit diagram to illustrate their operations.
This document discusses digital circuits and logic gates. It begins with an overview of analog and digital signals and the binary number system. It then covers Boolean algebra and how it is used to analyze logic gates. The three fundamental logic gates - OR, AND, and NOT - are explained through their truth tables and circuit implementations. More complex gates such as NOR, NAND, and XOR are also introduced and shown to be compositions of the fundamental gates. The document provides detailed explanations of each gate's symbol, truth table, and circuit to demonstrate how digital circuits perform logic operations.
1. The document discusses digital circuits and logic gates. It defines analog and digital signals and introduces the binary number system.
2. Boolean algebra and logic operations such as OR, AND, and NOT are described. The document provides truth tables to define the output of logic gates for all possible input combinations.
3. Common logic gates such as OR, AND, NOT, NOR, and NAND are defined. Their corresponding truth tables and circuit diagrams are given to illustrate how each gate implements Boolean logic operations. The gates can be combined to form other gates like XOR.
This document discusses digital logic gates and Boolean algebra. It defines the objectives as performing basic logic operations, describing AND, NAND, OR and NOR gates using truth tables, writing Boolean expressions, and implementing logic circuits. It explains Boolean constants and variables, the three basic logic operations (OR, AND, NOT), logic gates and their truth tables, gate IC numbers, and gives examples of implementing Boolean expressions as logic circuits.
Logic gates process true and false signals to perform logic functions. The key logic gates are NOT, AND, NAND, OR, NOR, EX-OR, and EX-NOR. Gates have standardized symbols and can be combined to create more complex logic functions. NAND and NOR gates are particularly useful because any other gate can be created by combining NAND or NOR gates.
perform operation with boolean algebraBrenda Debra
1. This document defines and explains the basic logic gates: NOT, AND, OR, NAND, NOR, EX-OR, and EX-NOR. It provides the logic symbol, truth table, and explains the output of each gate based on the input(s).
2. Examples of integrated circuits (ICs) that implement these basic logic gates are provided, such as the 7408 IC for AND gates and the 7404 IC for NOT gates.
3. At the end, there are exercises to develop truth tables for 3-input EX-OR and EX-NOR gates.
Digital logic circuits have two states - on or off (1 or 0, true or false). TTL uses bipolar transistors and operates at 5V but requires more power, while CMOS uses MOSFETs, operates at 3-15V, and consumes very little power, making it suitable for portable equipment. Sequential logic has an output dependent on current and previous inputs, while combinational logic only depends on current inputs. Basic logic gates include AND, OR, NAND, NOR, NOT, XOR, and XNOR.
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Logic gates
1. Logic Gates
Gate types: NOT | AND | NAND | OR | NOR | EX-OR | EX-NOR
Symbols | Truth tables | Logic ICs | Summary truth tables | Combinations | Substituting
Next Page: Capacitance and Uses of Capacitors
Also see: Logic ICs | 4000 Series | 74 Series
Logic states
True False
1 0
High Low
+Vs 0V
On Off
Introduction
Logic gates process signals which represent true or false. Normally the positive supply
voltage +Vs represents true and 0V represents false. Other terms which are used for the
true and false states are shown in the table on the right. It is best to be familiar with them
all.
Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-
NOR. Capital letters are normally used to make it clear that the term refers to a logic
gate.
Note that logic gates are not always required because simple logic functions can be
performed with switches or diodes:
• Switches in series (AND function)
• Switches in parallel (OR function)
• Combining chip outputs with diodes (OR function)
Logic gate symbols
There are two series of symbols for logic gates:
• The traditional symbols have distinctive shapes making them easy to recognise
so they are widely used in industry and education.
2. • The IEC (International Electrotechnical Commission) symbols are rectangles
with a symbol inside to show the gate function. They are rarely used despite their
official status, but you may need to know them for an examination.
Inputs and outputs
Gates have two or more inputs, except a NOT gate which has only one input. All gates
have only one output. Usually the letters A, B, C and so on are used to label inputs, and Q
is used to label the output. On this page the inputs are shown on the left and the output on
the right.
The inverting circle (o)
Some gate symbols have a circle on their output which means that their function includes
inverting of the output. It is equivalent to feeding the output through a NOT gate. For
example the NAND (Not AND) gate symbol shown on the right is the same as an AND
gate symbol but with the addition of an inverting circle on the output.
Input A Input B Output Q
0 0 0
0 1 0
1 0 0
1 1 1
Truth tables
A truth table is a good way to show the function of a logic gate. It shows the output states
for every possible combination of input states. The symbols 0 (false) and 1 (true) are
usually used in truth tables. The example truth table on the right shows the inputs and
output of an AND gate.
3. There are summary truth tables below showing the output
states for all types of 2-input and 3-input gates. These can be
helpful if you are trying to select a suitable gate.
Logic ICs
Logic gates are available on special ICs (chips) which usually contain several gates of the
same type, for example the 4001 IC contains four 2-input NOR gates. There are several
families of logic ICs and they can be split into two groups:
• 4000 Series
• 74 Series
To quickly compare the different families please see:
• Summary table of logic families
The 4000 and 74HC families are the best for battery powered projects because they will
work with a good range of supply voltages and they use very little power. However, if
you are using them to design circuits and investigate logic gates please remember that all
unused inputs MUST be connected to the power supply (either +Vs or 0V), this applies
even if that part of the IC is not being used in the circuit!
NOT gate (inverter)
The output Q is true when the input A is NOT true, the output is the inverse of the input:
Q = NOT A
A NOT gate can only have one input. A NOT gate is also called an inverter.
Input A Output Q
0 1
1 0
Traditional symbol IEC symbol Truth Table
AND gate
The output Q is true if input A AND input B are both true: Q = A AND B
An AND gate can have two or more inputs, its output is true if all inputs are true.
4. Input A Input B Output Q
0 0 0
0 1 0
1 0 0
1 1 1
Traditional symbol IEC symbol Truth Table
NAND gate (NAND = Not AND)
This is an AND gate with the output inverted, as shown by the 'o' on the output.
The output is true if input A AND input B are NOT both true: Q = NOT (A AND B)
A NAND gate can have two or more inputs, its output is true if NOT all inputs are true.
Input A Input B Output Q
0 0 1
0 1 1
1 0 1
1 1 0
Traditional symbol IEC symbol Truth Table
OR gate
The output Q is true if input A OR input B is true (or both of them are true): Q = A OR B
An OR gate can have two or more inputs, its output is true if at least one input is true.
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 1
Traditional symbol IEC symbol Truth Table
NOR gate (NOR = Not OR)
5. This is an OR gate with the output inverted, as shown by the 'o' on the output.
The output Q is true if NOT inputs A OR B are true: Q = NOT (A OR B)
A NOR gate can have two or more inputs, its output is true if no inputs are true.
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 0
Traditional symbol IEC symbol Truth Table
EX-OR (EXclusive-OR) gate
The output Q is true if either input A is true OR input B is true, but not when both of
them are true: Q = (A AND NOT B) OR (B AND NOT A)
This is like an OR gate but excluding both inputs being true.
The output is true if inputs A and B are DIFFERENT.
EX-OR gates can only have 2 inputs.
Input A Input B Output Q
0 0 0
0 1 1
1 0 1
1 1 0
Traditional symbol IEC symbol Truth Table
EX-NOR (EXclusive-NOR) gate
This is an EX-OR gate with the output inverted, as shown by the 'o' on the output.
The output Q is true if inputs A and B are the SAME (both true or both false):
Q = (A AND B) OR (NOT A AND NOT B)
EX-NOR gates can only have 2 inputs.
Input A Input B Output Q
0 0 1
0 1 0
1 0 0
1 1 1
6. Traditional symbol IEC symbol Truth Table
Summary truth tables
The summary truth tables below show the output states for all types of 2-input and 3-
input gates.
Summary for all 2-input gates Summary for all 3-input gates
Inputs Output of each gate Inputs Output of each gate
EX- EX- A B C AND NAND OR NOR
A B AND NAND OR NOR
OR NOR 0 0 0 0 1 0 1
0 0 0 1 0 1 0 1 0 0 1 0 1 1 0
0 1 0 1 1 0 1 0 0 1 0 0 1 1 0
1 0 0 1 1 0 1 0 0 1 1 0 1 1 0
1 1 1 0 1 0 0 1 1 0 0 0 1 1 0
1 0 1 0 1 1 0
1 1 0 0 1 1 0
Note that EX-OR and EX-NOR
gates can only have 2 inputs. 1 1 1 1 0 1 0
Combinations of logic gates
Input A Input B Output Q
0 0 0
0 1 0
1 0 1
1 1 0
Logic gates can be combined to produce more complex functions. They can also be
combined to substitute one type of gate for another.
For example to produce an output Q which is true only when input A is true and input B
is false, as shown in the truth table on the right, we can combine a NOT gate and an AND
gate like this:
7. Inputs Outputs
A B C D E Q
0 0 0 1 0 1
0 0 1 1 0 1
0 1 0 0 0 0
0 1 1 0 1 1
1 0 0 0 0 0
1 0 1 0 0 0
1 1 0 0 0 0
1 1 1 0 1 1
Q = A AND NOT B
Working out the function of a combination of gates
Truth tables can be used to work out the function of a combination of gates.
For example the truth table on the right show the intermediate outputs D and E as well as
the final output Q for the system shown below.
D = NOT (A OR B)
E = B AND C
Q = D OR E = (NOT (A OR B)) OR (B AND C)
Substituting one type of gate for another
8. Logic gates are available on ICs which usually contain several gates of the same type, for
example four 2-input NAND gates or three 3-input NAND gates. This can be wasteful if
only a few gates are required unless they are all the same type. To avoid using too many
ICs you can reduce the number of gate inputs or substitute one type of gate for another.
Reducing the number of inputs
The number of inputs to a gate can be reduced by connecting two (or more) inputs
together. The diagram shows a 3-input AND gate operating as a 2-input AND gate.
Making a NOT gate from a NAND or NOR gate
Reducing a NAND or NOR gate to just one input creates a NOT gate. The diagram
shows this for a 2-input NAND gate.
Any gate can be built from NAND or NOR gates
As well as making a NOT gate, NAND or NOR gates can be combined to create any type
of gate! This enables a circuit to be built from just one type of gate, either NAND or
NOR. For example an AND gate is a NAND gate then a NOT gate (to undo the inverting
function). Note that AND and OR gates cannot be used to create other gates because they
lack the inverting (NOT) function.
To change the type of gate, such as changing OR to AND, you must do three things:
• Invert (NOT) each input.
• Change the gate type (OR to AND, or AND to OR)
• Invert (NOT) the output.
For example an OR gate can be built from NOTed inputs fed into a NAND (AND +
NOT) gate.
NAND gate equivalents
The table below shows the NAND gate equivalents of NOT, AND, OR and NOR gates:
Gate Equivalent in NAND gates
NOT
9. AND
OR
NOR
Substituting gates in an example logic system
The original system has 3 different gates: NOR, AND and OR. This requires three ICs
(one for each type of gate).
To re-design this system using NAND gates only begin by replacing each gate with its
NAND gate equivalent, as shown in the diagram below.
10. Then simplify the system by deleting adjacent pairs of NOT gates (marked X above).
This can be done because the second NOT gate cancels the action of the first.
The final system is shown on the right. It has five NAND gates and requires two ICs
(with four gates on each IC). This is better than the original system which required three
ICs (one for each type of gate).
Substituting NAND (or NOR) gates does not always increase the number of gates, but
when it does (as in this example) the increase is usually only one or two gates. The real
benefit is reducing the number of ICs required by using just one type of gate.