- A signal is an electromagnetic or electrical current that carries data from one system to another. Signals can be either analog or digital.
- An analog signal has an infinite number of intensity levels over time, while a digital signal can only have a limited number of defined values, often 1 and 0.
- Logic gates are basic building blocks of digital circuits that perform logical operations. Common logic gates include AND, OR, NOT, NAND, NOR, XOR, and XNOR.
The document discusses computer organization and architecture. It provides details about logic gates, which are the basic building blocks of digital circuits. The seven basic logic gates are AND, OR, XOR, NOT, NAND, NOR and XNOR. Boolean algebra is used to analyze and simplify digital circuits. Karnaugh maps are a graphical technique to simplify Boolean expressions and minimize the number of variables. They allow grouping of variables to obtain the simplified sum of products or product of sums form.
Logic gates are basic building blocks of digital circuits that perform logical operations. The seven basic logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Boolean algebra uses binary numbers (0 and 1) and is used to analyze and simplify digital circuits. Karnaugh maps are a method to simplify Boolean functions by grouping adjacent 1's in a map based on the number of variables. This allows deriving the minimum number of terms to represent the function in sum-of-products form.
Boolean Aljabra.pptx of dld and computeritxminahil29
_Happiest birthday patner_"🥺❤️🤭
Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐
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Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐_Happiest birthday patner_"🥺❤️🤭
Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐
_JUG JUG JIYOOO_
_JUG JUG JIYOOO_
The document discusses logic gates and Boolean algebra. It defines key logic gate terms like AND, OR, NAND, NOR, and XOR gates. It provides truth tables that define the output of each gate based on all possible input combinations. Boolean algebra laws and operations are also covered, including addition, multiplication, commutative laws, associative laws, and the distributive law. Methods for converting between Boolean expressions, truth tables, and logic circuits are described. Examples are provided to illustrate how to derive the expression, truth table, or circuit from one of the other representations.
This document discusses logic gates and their truth tables. It begins by introducing basic logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR. It then provides details on each gate, including their symbols, truth tables and how they can be represented electrically. The document also discusses how gates can be connected together and how multi-input gates like 3-input and 4-input AND and OR gates work based on the same principles as 2-input gates. Finally, it notes that the output of one gate can be used as input to another, allowing logic circuits to be built from connected gates.
The document discusses universal gates and how NAND and NOR gates can be used to build any other logic gate. It provides examples of how to build AND, OR, NOT, XOR, and XNOR gates using only NAND or NOR gates. It also discusses combinational logic circuits including half adders, full adders, decoders, encoders, multiplexers and demultiplexers. Truth tables are provided for half adders and full adders.
This document provides an overview of a course on digital electronics that covers combinational and sequential logic. The course consists of 11 lectures and 6 hardware lab workshops. The objectives are for students to learn about combinational and sequential logic circuits, how digital logic gates are built using transistors, and how to design and construct simple digital electronic systems. Key topics that will be covered include Boolean algebra, logic gates, combinational logic, sequential logic, and how digital systems are constructed from semiconductors to computers. Recommended textbooks are also listed.
This document discusses computer organization and combinational circuits. It begins by defining logic gates as basic building blocks of digital circuits. The seven basic logic gates - AND, OR, XOR, NOT, NAND, NOR, and XNOR - are described along with their truth tables. Using combinations of these logic gates in arrays allows complex operations to be performed in combinational circuits like adders and subtractors. Half adders, full adders, n-bit parallel adders and subtractors are explained as examples of combinational circuits. Boolean algebra is also discussed as it relates to describing digital logic circuits in terms of true and false values.
The document discusses computer organization and architecture. It provides details about logic gates, which are the basic building blocks of digital circuits. The seven basic logic gates are AND, OR, XOR, NOT, NAND, NOR and XNOR. Boolean algebra is used to analyze and simplify digital circuits. Karnaugh maps are a graphical technique to simplify Boolean expressions and minimize the number of variables. They allow grouping of variables to obtain the simplified sum of products or product of sums form.
Logic gates are basic building blocks of digital circuits that perform logical operations. The seven basic logic gates are AND, OR, NOT, NAND, NOR, XOR, and XNOR. Boolean algebra uses binary numbers (0 and 1) and is used to analyze and simplify digital circuits. Karnaugh maps are a method to simplify Boolean functions by grouping adjacent 1's in a map based on the number of variables. This allows deriving the minimum number of terms to represent the function in sum-of-products form.
Boolean Aljabra.pptx of dld and computeritxminahil29
_Happiest birthday patner_"🥺❤️🤭
Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐
_JUG JUG JIYOOO__Happiest birthday patner_"🥺❤️🤭
Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐_Happiest birthday patner_"🥺❤️🤭
Many many happy returns of the day ❤️🌏🔐.... may this year brings more happiness 🤗 and success 🥀 for u..... may uh have many more 🥰🫶.... may urhh life be as beautiful as you are 😋🌏🫀..... may ur all desire wishes come true 😌✨🖤..... May uh get double of everything uh want in ur life 🌈💫......you're such a great guy and puri hearted and sweetest girl 🥹🫰🏻🩷....uh deserve all cakes hug an happiness today 🥰👻... hmesha khush rho pyariiii🫣🩷....
Once again happy birthday My Gurl 🥳❤️🔐
_JUG JUG JIYOOO_
_JUG JUG JIYOOO_
The document discusses logic gates and Boolean algebra. It defines key logic gate terms like AND, OR, NAND, NOR, and XOR gates. It provides truth tables that define the output of each gate based on all possible input combinations. Boolean algebra laws and operations are also covered, including addition, multiplication, commutative laws, associative laws, and the distributive law. Methods for converting between Boolean expressions, truth tables, and logic circuits are described. Examples are provided to illustrate how to derive the expression, truth table, or circuit from one of the other representations.
This document discusses logic gates and their truth tables. It begins by introducing basic logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR. It then provides details on each gate, including their symbols, truth tables and how they can be represented electrically. The document also discusses how gates can be connected together and how multi-input gates like 3-input and 4-input AND and OR gates work based on the same principles as 2-input gates. Finally, it notes that the output of one gate can be used as input to another, allowing logic circuits to be built from connected gates.
The document discusses universal gates and how NAND and NOR gates can be used to build any other logic gate. It provides examples of how to build AND, OR, NOT, XOR, and XNOR gates using only NAND or NOR gates. It also discusses combinational logic circuits including half adders, full adders, decoders, encoders, multiplexers and demultiplexers. Truth tables are provided for half adders and full adders.
This document provides an overview of a course on digital electronics that covers combinational and sequential logic. The course consists of 11 lectures and 6 hardware lab workshops. The objectives are for students to learn about combinational and sequential logic circuits, how digital logic gates are built using transistors, and how to design and construct simple digital electronic systems. Key topics that will be covered include Boolean algebra, logic gates, combinational logic, sequential logic, and how digital systems are constructed from semiconductors to computers. Recommended textbooks are also listed.
This document discusses computer organization and combinational circuits. It begins by defining logic gates as basic building blocks of digital circuits. The seven basic logic gates - AND, OR, XOR, NOT, NAND, NOR, and XNOR - are described along with their truth tables. Using combinations of these logic gates in arrays allows complex operations to be performed in combinational circuits like adders and subtractors. Half adders, full adders, n-bit parallel adders and subtractors are explained as examples of combinational circuits. Boolean algebra is also discussed as it relates to describing digital logic circuits in terms of true and false values.
This document discusses Boolean algebra and logic gates. It defines Boolean algebra as having two values - True or False. Logic circuits in computers are also designed to have two states - high (1) or low (0). The three basic Boolean operators are AND, OR, and NOT. Truth tables represent all possible combinations of variable values in a Boolean expression. Common logic gates like AND, OR, and NOT are used to implement Boolean functions and are the building blocks of digital circuits. DeMorgan's theorems relate Boolean operations and their complements.
This document provides an overview of switching theory unit 2, which covers combinational logic circuits and their design procedures. It discusses various combinational logic components like adders, subtractors, multiplexers, demultiplexers, encoders, and decoders. It provides block diagrams, truth tables, and logic expressions for designing these components. The key topics covered include the characteristics of combinational circuits, the 4-step design procedure for any combinational circuit, implementation of full adders and subtractors, working of multiplexers and demultiplexers of different sizes, and working of encoders and decoders.
- Boolean algebra uses binary numbers (0 and 1) and logical operations (AND, OR, NOT) to analyze and simplify digital circuits.
- It was invented by George Boole in 1854 and represents variables that can be either 1 or 0.
- The document discusses Boolean operations, laws, logic gates, minimization techniques, and representing functions as sums of products.
Number Systems - Arithmetic Operations - Binary Codes- Boolean Algebra and Logic Gates - Theorems and Properties of Boolean Algebra - Boolean Functions - Canonical and Standard Forms - Simplification of Boolean Functions using Karnaugh Map - Logic Gates – NAND and NOR Implementations.
This document provides an overview of Boolean algebra, which describes logical relations and operations in digital circuits. It discusses:
1) George Boole's rules that describe logical propositions as either true or false, which can represent digital circuit states of 1 or 0.
2) Basic Boolean operations like AND, OR, and NOT and how they are represented by logic gates. Truth tables show all possible input/output combinations for each gate.
3) Laws of Boolean algebra like commutativity, association, distribution, and others. Karnaugh maps provide a way to simplify Boolean expressions into sum-of-products form.
The document discusses Boolean algebra and logic gates. It defines logic gates, explains their operations, and provides their logic symbols and truth tables. The types of logic gates covered are AND, OR, NOT, NOR, NAND, XOR, and XNOR. It also discusses sequential logic circuits like flip-flops, providing details on SR, JK, T, and D flip-flops including how to build them using logic gates. Additional topics covered include the difference between combinational and sequential logic circuits, Boolean theorems, sum-of-products and product-of-sums expressions, and the Karnaugh map method for simplifying logic expressions.
Combinational circuits are digital circuits whose outputs depend only on the current inputs. They do not have internal memory and include common components like multiplexers, decoders, and adders. A combinational circuit with n inputs can have up to 2^n possible output combinations. Common combinational circuits discussed in the document include half adders, full adders, decoders, and multiplexers along with their truth tables and applications. Sequential circuits differ in that their outputs depend on both current and previous inputs due to internal memory elements like latches and flip-flops.
CDMA allows multiple communication channels to share the same frequency band by using unique coded signals called orthogonal codes or Walsh codes. Each station transmitting data is assigned a unique orthogonal code. The codes are multiplied with the data bits and combined at the transmitter. At the receiver, the combined signal is multiplied by each possible code. If it matches the code assigned to that station, the data bit value can be recovered. Using orthogonal codes in this way allows separation of the multiple communication channels in the shared frequency band.
Most modern devices are made from billions of on /off switches called transistors
We will build a processor in this course!
Transistors made from semiconductor materials:
MOSFET – Metal Oxide Semiconductor Field Effect Transistor
NMOS, PMOS – Negative MOS and Positive MOS
CMOS – Complimentary MOS made from PMOS and NMOS transistors
Transistors used to make logic gates and logic circuits
We can now implement any logic circuit
Can do it efficiently, using Karnaugh maps to find the minimal terms required
Can use either NAND or NOR gates to implement the logic circuit
Can use P- and N-transistors to implement NAND or NOR gates
This document provides an overview of digital logic gates. It discusses basic gates like AND, OR, and NOT and derived gates like NAND, NOR, XOR, and XNOR. For each gate, it describes the boolean expression, symbol, equivalent circuit, and truth table. The basic gates perform logical operations using simple boolean expressions while the derived gates combine basic gates to perform more complex operations. The document aims to review the fundamental digital logic gates used in digital electronics and circuits.
The document provides an overview of digital electronics circuits and topics that will be covered in 3 modules. Module 1 introduces various number systems and their conversions. It also covers Boolean algebra, logic gates, Karnaugh maps. Module 2 discusses combinational logic design including half/full adders, decoders, multiplexers. Module 3 covers sequential logic including flip-flops, counters, shift registers, memory and programmable logic. The document outlines the contents to introduce digital electronics circuits concepts.
This document discusses simplification of circuits through Demorgan's theorem and Karnaugh maps. It begins with an introduction and table of contents. It then covers Demorgan's theorem, proving it using truth tables. It also discusses simplification using Boolean laws and defines various Boolean logic terms. The document covers Karnaugh maps for 2, 3, and 4 variables and how to simplify using them. It also discusses logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR gates through their truth tables and diagrams. Finally, it covers DeMorgan's theorems, proving them using truth tables and logic gates.
This document discusses Boolean logic and logic gates. It describes the basic logic gates - NOT, AND, and OR - and how more complex gates like NAND and NOR are derived from them. It also covers Boolean logic concepts like duality, De Morgan's theorems, and how logic gates can be combined into circuits to perform decision making and memory functions. Applications of logic gates include systems for genetic engineering, nanotechnology, industrial processes and medicine.
Logic gates are electronic circuits that perform basic logical operations and form the building blocks of digital circuits. The document discusses different types of logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR. It explains their truth tables and Boolean expressions. It also talks about how logic gates are implemented using transistors and their use in basic circuits like flip-flops that form the basis of computer memory.
This document provides an introduction to digital electronics and digital systems. It discusses the differences between analog and digital systems, with digital systems using discrete binary values of 1 and 0 rather than continuous values. The advantages of digital systems include ease of programmability, lower costs, higher speeds and reliability. Number systems are also introduced, including binary, octal, hexadecimal and binary coded decimal. Techniques for minimizing boolean expressions using Karnaugh maps are described through examples. Finally, boolean algebra and the laws used for simplifying boolean expressions are covered.
This document provides an overview of digital logic circuits and digital systems. It discusses binary logic, logic gates like NAND and NOR, Boolean algebra, decoders, adders, and the differences between analog and digital signals. It also covers representations of digital designs using truth tables, Boolean algebra, logic gate schematics, and logic simulations. Common logic gates, functions, identities, simplification techniques, and the duality principle of Boolean algebra are described.
The document discusses different types of shift registers and counters. It describes serial-in serial-out, serial-in parallel-out, parallel-in serial-out, and parallel-in parallel-out shift registers. It also covers asynchronous and synchronous counters such as ripple counters, up/down counters, and mod-N counters. Diagrams and truth tables are provided to illustrate the working of different shift registers and counters.
The document discusses latches and flip-flops. It describes SR latches and how they can be used to make SR flip-flops. It then discusses different types of flip-flops including D, JK, T flip-flops. It explains how SR flip-flops can be converted to these other flip-flops and discusses issues like race conditions in JK flip-flops and how master-slave flip-flops address this issue.
This document discusses Boolean algebra and logic gates. It defines Boolean algebra as having two values - True or False. Logic circuits in computers are also designed to have two states - high (1) or low (0). The three basic Boolean operators are AND, OR, and NOT. Truth tables represent all possible combinations of variable values in a Boolean expression. Common logic gates like AND, OR, and NOT are used to implement Boolean functions and are the building blocks of digital circuits. DeMorgan's theorems relate Boolean operations and their complements.
This document provides an overview of switching theory unit 2, which covers combinational logic circuits and their design procedures. It discusses various combinational logic components like adders, subtractors, multiplexers, demultiplexers, encoders, and decoders. It provides block diagrams, truth tables, and logic expressions for designing these components. The key topics covered include the characteristics of combinational circuits, the 4-step design procedure for any combinational circuit, implementation of full adders and subtractors, working of multiplexers and demultiplexers of different sizes, and working of encoders and decoders.
- Boolean algebra uses binary numbers (0 and 1) and logical operations (AND, OR, NOT) to analyze and simplify digital circuits.
- It was invented by George Boole in 1854 and represents variables that can be either 1 or 0.
- The document discusses Boolean operations, laws, logic gates, minimization techniques, and representing functions as sums of products.
Number Systems - Arithmetic Operations - Binary Codes- Boolean Algebra and Logic Gates - Theorems and Properties of Boolean Algebra - Boolean Functions - Canonical and Standard Forms - Simplification of Boolean Functions using Karnaugh Map - Logic Gates – NAND and NOR Implementations.
This document provides an overview of Boolean algebra, which describes logical relations and operations in digital circuits. It discusses:
1) George Boole's rules that describe logical propositions as either true or false, which can represent digital circuit states of 1 or 0.
2) Basic Boolean operations like AND, OR, and NOT and how they are represented by logic gates. Truth tables show all possible input/output combinations for each gate.
3) Laws of Boolean algebra like commutativity, association, distribution, and others. Karnaugh maps provide a way to simplify Boolean expressions into sum-of-products form.
The document discusses Boolean algebra and logic gates. It defines logic gates, explains their operations, and provides their logic symbols and truth tables. The types of logic gates covered are AND, OR, NOT, NOR, NAND, XOR, and XNOR. It also discusses sequential logic circuits like flip-flops, providing details on SR, JK, T, and D flip-flops including how to build them using logic gates. Additional topics covered include the difference between combinational and sequential logic circuits, Boolean theorems, sum-of-products and product-of-sums expressions, and the Karnaugh map method for simplifying logic expressions.
Combinational circuits are digital circuits whose outputs depend only on the current inputs. They do not have internal memory and include common components like multiplexers, decoders, and adders. A combinational circuit with n inputs can have up to 2^n possible output combinations. Common combinational circuits discussed in the document include half adders, full adders, decoders, and multiplexers along with their truth tables and applications. Sequential circuits differ in that their outputs depend on both current and previous inputs due to internal memory elements like latches and flip-flops.
CDMA allows multiple communication channels to share the same frequency band by using unique coded signals called orthogonal codes or Walsh codes. Each station transmitting data is assigned a unique orthogonal code. The codes are multiplied with the data bits and combined at the transmitter. At the receiver, the combined signal is multiplied by each possible code. If it matches the code assigned to that station, the data bit value can be recovered. Using orthogonal codes in this way allows separation of the multiple communication channels in the shared frequency band.
Most modern devices are made from billions of on /off switches called transistors
We will build a processor in this course!
Transistors made from semiconductor materials:
MOSFET – Metal Oxide Semiconductor Field Effect Transistor
NMOS, PMOS – Negative MOS and Positive MOS
CMOS – Complimentary MOS made from PMOS and NMOS transistors
Transistors used to make logic gates and logic circuits
We can now implement any logic circuit
Can do it efficiently, using Karnaugh maps to find the minimal terms required
Can use either NAND or NOR gates to implement the logic circuit
Can use P- and N-transistors to implement NAND or NOR gates
This document provides an overview of digital logic gates. It discusses basic gates like AND, OR, and NOT and derived gates like NAND, NOR, XOR, and XNOR. For each gate, it describes the boolean expression, symbol, equivalent circuit, and truth table. The basic gates perform logical operations using simple boolean expressions while the derived gates combine basic gates to perform more complex operations. The document aims to review the fundamental digital logic gates used in digital electronics and circuits.
The document provides an overview of digital electronics circuits and topics that will be covered in 3 modules. Module 1 introduces various number systems and their conversions. It also covers Boolean algebra, logic gates, Karnaugh maps. Module 2 discusses combinational logic design including half/full adders, decoders, multiplexers. Module 3 covers sequential logic including flip-flops, counters, shift registers, memory and programmable logic. The document outlines the contents to introduce digital electronics circuits concepts.
This document discusses simplification of circuits through Demorgan's theorem and Karnaugh maps. It begins with an introduction and table of contents. It then covers Demorgan's theorem, proving it using truth tables. It also discusses simplification using Boolean laws and defines various Boolean logic terms. The document covers Karnaugh maps for 2, 3, and 4 variables and how to simplify using them. It also discusses logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR gates through their truth tables and diagrams. Finally, it covers DeMorgan's theorems, proving them using truth tables and logic gates.
This document discusses Boolean logic and logic gates. It describes the basic logic gates - NOT, AND, and OR - and how more complex gates like NAND and NOR are derived from them. It also covers Boolean logic concepts like duality, De Morgan's theorems, and how logic gates can be combined into circuits to perform decision making and memory functions. Applications of logic gates include systems for genetic engineering, nanotechnology, industrial processes and medicine.
Logic gates are electronic circuits that perform basic logical operations and form the building blocks of digital circuits. The document discusses different types of logic gates like AND, OR, NOT, NAND, NOR, XOR and XNOR. It explains their truth tables and Boolean expressions. It also talks about how logic gates are implemented using transistors and their use in basic circuits like flip-flops that form the basis of computer memory.
This document provides an introduction to digital electronics and digital systems. It discusses the differences between analog and digital systems, with digital systems using discrete binary values of 1 and 0 rather than continuous values. The advantages of digital systems include ease of programmability, lower costs, higher speeds and reliability. Number systems are also introduced, including binary, octal, hexadecimal and binary coded decimal. Techniques for minimizing boolean expressions using Karnaugh maps are described through examples. Finally, boolean algebra and the laws used for simplifying boolean expressions are covered.
This document provides an overview of digital logic circuits and digital systems. It discusses binary logic, logic gates like NAND and NOR, Boolean algebra, decoders, adders, and the differences between analog and digital signals. It also covers representations of digital designs using truth tables, Boolean algebra, logic gate schematics, and logic simulations. Common logic gates, functions, identities, simplification techniques, and the duality principle of Boolean algebra are described.
The document discusses different types of shift registers and counters. It describes serial-in serial-out, serial-in parallel-out, parallel-in serial-out, and parallel-in parallel-out shift registers. It also covers asynchronous and synchronous counters such as ripple counters, up/down counters, and mod-N counters. Diagrams and truth tables are provided to illustrate the working of different shift registers and counters.
The document discusses latches and flip-flops. It describes SR latches and how they can be used to make SR flip-flops. It then discusses different types of flip-flops including D, JK, T flip-flops. It explains how SR flip-flops can be converted to these other flip-flops and discusses issues like race conditions in JK flip-flops and how master-slave flip-flops address this issue.
The document discusses various digital logic circuits including half adders, full adders, parallel adders, subtractors, multiplexers, demultiplexers, encoders, and decoders. It explains the basic concepts and provides examples of implementing 1-bit, 2-bit, 4-bit, and 8-bit versions of these circuits using logic gates like AND, OR, and NOT. Implementation of higher order multiplexers and decoders using lower order building blocks is also covered.
This document discusses various data types in C programming language. It begins by defining what a data type is and then provides examples of common data types like char, int, float, and double. It explains that each data type requires a different amount of memory and has an associated range for storing values. The document then provides a table listing the typical ranges and memory requirements for each data type on a 32-bit compiler. It also includes an example C program demonstrating the usage of different data types.
The document provides an introduction to compiler design, including:
- A compiler converts a program written in a high-level language into machine code. It can run on a different machine than the target.
- Language processing systems like compilers transform high-level code into a form usable by machines through a series of translations.
- A compiler analyzes source code in two main phases - analysis and synthesis. The analysis phase creates an intermediate representation, and the synthesis phase generates target code from that.
- XML (eXtensible Markup Language) is a markup language that is designed to store and transport data. It was released in the late 1990s and became a W3C recommendation in 1998.
- XML is not meant to display data like HTML, but rather to carry data. It is designed to be self-descriptive, platform independent, and language independent. Tags are defined by the user rather than being predefined.
- A markup language uses tags to highlight or underline parts of a document. Modern markup languages like XML use tags to replace highlighting and underlining.
The document provides information about Dynamic Hypertext Markup Language (DHTML). It discusses that DHTML is not a language itself but a combination of technologies including HTML, CSS, JavaScript, and DOM to make web pages dynamic and interactive. It then explains the four main components of DHTML and provides examples of using JavaScript, DOM, events, and CSS to manipulate HTML elements and create dynamic content. The document also covers advantages and disadvantages of DHTML.
The document discusses different image file formats including JPEG, GIF, and PNG. It describes the advantages and disadvantages of each format, noting that JPEG is best for photos while GIF and PNG are better for web use due to support for animation and transparency. The document also covers the differences between server-side and client-side scripting, and provides examples of each. Common JavaScript concepts like data types, operators, loops, and functions are defined. Methods for creating objects and arrays in JavaScript are presented.
The <frame> tag in HTML is used to divide the browser window into multiple frames. Each frame displays a separate HTML document and the tags are not supported in HTML5 as frames cause accessibility and usability issues. Frames were commonly used in the past to divide web pages for navigation menus, headers/footers and content but have been replaced by CSS for layout.
Automata theory deals with logic of computation using simple machines called automata. Automata enables understanding how machines compute functions and solve problems. The main concepts are strings, languages, finite automata, regular expressions, and regular grammars. Finite automata recognize patterns in input strings and transition between states, accepting or rejecting strings. Deterministic finite automata (DFAs) uniquely transition to one state for each input, while non-deterministic finite automata (NFAs) can transition to multiple states. Regular expressions and regular grammars also define regular languages recognized by finite automata.
CSS (Cascading Style Sheets) is a style sheet language used to describe the presentation of HTML documents, including how elements are displayed on screen, paper, or in other media. The document discusses various CSS properties such as display, background, border, and their values and usage. CSS can control the layout, formatting, and styles of HTML elements and is commonly used alongside HTML and JavaScript to create visually appealing web pages and user interfaces.
The document discusses memory organization and hierarchy in a computer system. It explains that memory hierarchy is used to minimize access time by organizing memory such that frequently used parts are closer to the CPU. It describes the different levels of memory including main memory, cache memory, and auxiliary memory. It provides details on RAM, ROM, and how the computer starts up using the bootstrap loader stored in ROM. It also discusses associative memory and different mapping techniques used to transfer data between main and cache memory such as direct mapping and set-associative mapping.
The document discusses addition, subtraction, multiplication, and division algorithms for signed binary numbers. It describes the process for each operation step-by-step including comparing sign bits, performing the operation, and determining the final result. Hardware implementations for addition/subtraction and multiplication are also covered, showing how the algorithms can be physically realized using components like registers, adders, and shift registers.
The document discusses microprogrammed control in CPUs. It explains that the control unit can be implemented using either hardwired logic or microcode. Microprogramming allows flexible control by storing sequences of microoperations in a control memory. It describes the components of a CPU like registers, ALU, and buses. Common microoperations like push/pop on a register stack are also summarized.
This document discusses register transfer and microoperations. It defines registers, their designations, and how information is transferred between registers. A microoperation is an elementary operation performed on data stored in registers, such as shift, count, clear, and load. Information can be transferred between registers using a replacement operator like R2<-R1. Control functions with conditions like if P=1 can control when a transfer occurs. The document also discusses arithmetic microoperations like addition, subtraction, incrementing and decrementing registers. Binary adders and arithmetic circuits are shown for implementing addition and subtraction.
Testing web applications presents unique challenges compared to traditional software testing. Key areas for web application testing include functionality, user interface, navigation, forms, browser compatibility, security, performance via load and stress testing, databases, and metrics. Thorough testing is needed to ensure applications work across different devices, browsers, and environments with varying bandwidths and firewalls. Web application testing aims to evaluate the application's usability, response time, and ability to handle traffic spikes while providing accurate information to users.
Unit testing involves testing individual software units or modules independently. Integration testing combines units and tests their interfaces and interactions. System testing evaluates the full system against requirements. Acceptance testing is done by customers to determine if they will accept the final product. There are four levels of testing - unit testing, integration testing, system testing, and acceptance testing - each with specific objectives to test the software at different stages.
This document discusses various functional testing techniques, including:
- Boundary value analysis, which tests inputs at minimum, maximum, and nominal values to find faults.
- Equivalence class testing, which divides the input domain into classes and tests one representative from each class.
- Decision table testing, which represents logical relationships between inputs and outputs in a table to derive test cases.
The techniques aim to design test cases that have a higher probability of failure and cover all possible program functionality through a black box approach. Functional testing treats the program as a black box and ignores internal structure.
- "Testing is the process of executing a program with the intent of finding faults."
- Good testing involves more than just executing a program a few times, including testing all possible paths and inputs. However, exhaustive testing of everything is impossible due to constraints.
- The costs of fixing errors increases drastically from early phases like specification to later phases like testing and maintenance. Early testing helps find errors at lower cost.
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2. What is Signal?
• A signal is an electromagnetic or electrical
current that is used for carrying data from
one system or network to another.
• In electronics and telecommunications, it
refers to any time-varying voltage that is
an electromagnetic wave which carries
information.
• There are two main types of signals:
Analog signal and Digital signal.
3. Analog and Digital Signals
• Like the data they represent, signals can be either
analog or digital.
• An analog signal has infinitely many levels of
intensity over a period of time.
• As the wave moves from value A to value B, it
passes through and includes an infinite number
of values along its path.
• A digital signal, on the other hand, can have only
a limited number of defined values.
• Although each value can be any number, it is
often as simple as 1 and O.
• The simplest way to show signals is by plotting
them on a pair of perpendicular axes.
Made By : Mr Himanshu Pabbi 3
4. • The vertical axis represents the value or
strength of a signal.
• The horizontal axis represents time. Figure 3.1
illustrates an analog signal and a digital signal.
• The curve representing the analog signal
passes through an infinite number of points.
• The vertical lines of the digital signal, however,
demonstrate the sudden jump that the signal
makes from value to value.
Made By : Mr Himanshu Pabbi 4
7. • Analog signal is a continuous signal in
which one time-varying quantity
represents another time-based
variable.
• These kind of signals works with
physical values and natural phenomena
such as earthquake, frequency,
volcano, speed of wind, weight,
lighting, etc.
8.
9. • A digital signal is a signal that is used
to represent data as a sequence of
separate values at any point in time.
• It can only take on one of a fixed
number of values.
• This type of signal represents a real
number within a constant range of
values.
• Now, let’s learn some key difference
between Digital and Analog signals.
10.
11. • A logic gate is a device that acts as a building
block for digital circuits.
• They perform basic logical functions that are
fundamental to digital circuits.
• Most electronic devices we use today will
have some form of logic gates in them
12. Logic Gates
• The seven basic logic gates includes: AND, OR,
XOR, NOT, NAND, NOR, and XNOR.
• The relationship between the input-output
binary variables for each gate can be
represented in tabular form by a truth table.
• Each gate has one or two binary input
variables designated by A and B and one
binary output variable designated by x.
13. AND GATE
• The AND gate is an electronic circuit which
gives a high output only if all its inputs are
high.
• The AND operation is represented by a dot (.)
sign.
14. OR GATE
• The OR gate is an electronic circuit which gives
a high output if one or more of its inputs are
high.
• The operation performed by an OR gate is
represented by a plus (+) sign.
15.
16. NAND GATE
• The NOT-AND (NAND) gate which is equal to
an AND gate followed by a NOT gate.
• The NAND gate gives a high output if any of
the inputs are low.
• The NAND gate is represented by a AND gate
with a small circle on the output.
• The small circle represents inversion.
17.
18. NOR GATE
• The NOT-OR (NOR) gate which is equal to an
OR gate followed by a NOT gate.
• The NOR gate gives a low output if any of the
inputs are high.
• The NOR gate is represented by an OR gate
with a small circle on the output.
• The small circle represents inversion.
19.
20. Exclusive-OR/ XOR GATE
• The 'Exclusive-OR' gate is a circuit which will
give a high output if one of its inputs is high
but not both of them.
• The XOR operation is represented by an
encircled plus sign.
21. EXCLUSIVE-NOR/Equivalence GATE
• The 'Exclusive-NOR' gate is a circuit that does
the inverse operation to the XOR gate.
• It will give a low output if one of its inputs is
high but not both of them.
• The small circle represents inversion.
22.
23. 2015
• What are universal gate? obtain EX-OR
operation with universal gates(3.5 marks)
24. Universal Logic Gates
• NAND and NOR are also known as universal
gates since they can be used to implement
any digital circuit without using any other
gate.
• This means that every gate can be created by
NAND or NOR gates only.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35. NOTE
• In nand inputs are given complement and in
nor inputs are given normal to design circuit
38. Boolean Algebra
• Boolean Algebra is used to analyze and
simplify the digital (logic) circuits.
• It uses only the binary numbers i.e. 0 and 1.
• It is also called as Binary Algebra or logical
Algebra.
• Boolean algebra was invented by George
Boole in 1854.
39. Rule in Boolean Algebra
• Boolean Algebra is used to analyze and
simplify the digital (logic) circuits.
• It uses only the binary numbers i.e. 0 and 1.
• It is also called as Binary Algebra or logical
Algebra.
• Boolean algebra was invented by George
Boole in 1854.
45. Reduce the following Boolean expression
(A+B+C)(A+B’+C)(A+B+C’)
Sol: A+B=X
(X+C)(A+B’+C)(X+C’)
(X+C)(X+C’)(A+B’+C)
Using distributive law we can write
(X+C.C’)(A+B’+C)
C.C’=0 so we get
(X)(A+B’+C)
Now replace X by A+B
(A+B).(A+B’+C)
74. • Representation of Boolean expression can be
primarily done in two ways. They are as
follows:
1. Sum of Products (SOP) form
2. Product of Sums (POS) form
100. Product of Sums (POS)
• As the name suggests, it is formed by
multiplying(AND operation) the sum terms.
• These sum terms are also called as ‘max-
terms’.
• Max-terms are represented with ‘M’, they are
the sum (OR operation) of Boolean variables
either in normal form or complemented form.
101.
102.
103. • While writing POS, the following convention is
to be followed:
104.
105. Introduction of K-Map (Karnaugh
Map)
• We can minimize Boolean expressions of 3, 4
variables very easily using K-map without
using any Boolean algebra theorems.
• K-map can take two forms Sum of Product
(SOP) and Product of Sum (POS) according to
the need of problem.
• K-map is table like representation but it gives
more information than TRUTH TABLE.
• We fill grid of K-map with 0’s and 1’s then
solve it by making groups.
106. K-Map (Karnaugh Map)
Steps to solve expression using K-map
1. Select K-map according to the number of
variables.
2. Identify minterms or maxterms as given in
problem.
3. For SOP put 1’s in blocks of K-map respective
to the minterms (0’s elsewhere).
4. For POS put 0’s in blocks of K-map respective
to the maxterms (1’s elsewhere).
107. • In K-map, the number of cells is similar to
the total number of variable input
combinations.
• For example, if the number of variables
is three, the number of cells is 23=8, and
• if the number of variables is four, the
number of cells is 24.
108. 5. Make rectangular groups containing total
terms in power of two like 2,4,8 ..(except 1) and
try to cover as many elements as you can in one
group.
6. From the groups made in step 5 find the
product terms and sum them up for SOP form.
109.
110.
111.
112.
113.
114.
115.
116.
117. 2 Variable K-map
• There is a total of 4 variables in a 2-
variable K-map.
• The following figure shows the structure of
the 2-variable K-map
123. 3-variable K-map
• The 3-variable K-map is represented as an array
of eight cells.
• In this case, we used A, B, and C for the variable.
• We can use any letter for the names of the
variables.
• The binary values of variables A and B are along
the left side, and the values of C are across the
top.
• The value of the given cell is the binary values of A
and B at left side in the same row combined with
the value of C at the top in the same column.
• For example, the cell in the upper left corner has a
binary value of 000, and the cell in the lower right
corner has a binary value of 101.
127. • From red group we get product term—
A’C
• From green group we get product term—
AB
• Summing these product terms we get- Final
expression (A’C+AB)
128.
129. The 4-Variable Karnaugh Map
• The 4-variable K-map is represented as an
array of 16 cells.
• Binary values of A and B are along the left
side, and the values of C and D are across
the top.
• The value of the given cell is the binary
values of A and B at left side in the same row
combined with the binary values of C and D
at the top in the same column.
• For example, the cell in the upper right corner
has a binary value of 0010, and the cell in the
133. K-map for 4 variables
F(P,Q,R,S)=∑(0,2,5,7,8,10,13,15)
134. • From red group we get product term—
QS
• From green group we get product term—
Q’S’
• Summing these product terms we get-
• Final expression (QS+Q’S’)
142. Don't Care Condition
• The "Don't care" condition says that we can use
the blank cells of a K-map to make a group of the
variables. To make a group of cells, we can use
the "don't care" cells as either 0 or 1, and if
required, we can also ignore that cell.
• We mainly use the "don't care" cell to make a
large group of cells.
• The cross(×) symbol is used to represent the
"don't care" cell in K-map. This cross symbol
represents an invalid combination. The "don't
care" in excess-3 code are 0000, 0001, 0010,
1101, 1110, and 1111 because they are invalid
combinations.
• Apart from this, the 4-bit BCD to Excess-3 code,
the "don't care" are 1010, 1011, 1100, 1101, 1110,
and 1111.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153. • We can change the standard SOP function
into a POS expression by making the
"don't care" terms the same as they are.
The missing minterms of the POS form are
written as maxterms of the POS form. In
the same way, we can change the
standard POS function into an SOP
expression by making the "don't care"
terms the same as they are. The missing
maxterms of the SOP form are written as
minterm of the SOP form
154.
155. Number System and Base Conversions
• Electronic and Digital systems may use a
variety of different number systems, (e.g.
Decimal, Hexadecimal, Octal, Binary).
• A number N in base or radix b can be written
as:
(N)b = dn-1 dn-2 — — — — d1 d0 . d-1 d-2 — — —
— d-m
• In the above, dn-1 to d0 is integer part, then
follows a radix point, and then d-1 to d-m is
fractional part.
• dn-1 = Most significant bit (MSB)
157. • An Octal Number or oct for short is the base-8
number and uses the digits 0 to 7.
• Octal numerals can be made from binary
numerals by grouping consecutive binary
digits into groups of three (starting from the
right).
• A Hexadecimal Number is a positional
numeral system with a radix, or base, of 16
and uses sixteen distinct symbols.
• It may be a combination of alphabets and
numbers.
• It uses numbers from 0 to 9 and alphabets A
to F.
158. • Decimal Number System :
If the Base value of a number system is
10. This is also known as base-10 number
system which has 10 symbols, these are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Position of every
digit has a weight which is a power of 10.
159.
160. How to convert a number from one
base to another?
1. Decimal to Binary
161. • Note: Keep multiplying the fractional part
with 2 until decimal part 0.00 is obtained.
(0.25)10 = (0.01)2
• Answer: (10.25)10 = (1010.01)2
162.
163. How to Convert from Binary to
Decimal?
• To convert a binary number to decimal we
need to perform a multiplication operation
on each digit of a binary number from right
to left with powers of 2 starting from 0 and
add each result to get the decimal number
of it.
184. Excess-3 Code
• In Excess-3 code, 3 is added to the individual
digit of a decimal number then these binary
equivalent are written.
• Excess-3 binary code is the only unweighted
self-complementary BCD code.
• Self-Complementary property means that the
1’s complement of an excess-3 number is the
excess-3 code of the 9’s complement of the
corresponding decimal number.
186. Example
• XS-3 code for decimal number 24
• In BCD
• 2=0010
• 4=0100
Now we will add 3 to both
2+3=5 0101
4+3=7 0111
X-3 code for 24= 0101 0111
187. Self complement Excess-3 code
Complement of 0 =9
Complement of 1=8
Complement of 3=7
Complement of 4=6
Complement of 5=5
Excess-3 is only unweight code which is self
complementing code.
188. Short cut to check if code is self
complementing or not
Is 8-4-2-1 a self complementing code?
If sum is 9 it is self complementing code
8+4+2+1=15!=9 so 8-4-2-1 code is not self
complementing code.
Is 2-4-2-1 is a self complementing code?
2+4+2+1=9=9 so it is self complementing code
189. 2015
• What is gray code? Why it is important? List
features of BCD and Excess-3 codes(6 marks)
190. GRAY Code
• The gray code is a binary code.
• The binary bits are arranged in such a way
that only one binary bit changes at a time
when we make a change from any number to
the next.
• Uses of Gray codes
• Gray codes are used in Karnaugh maps.
191.
192. Explanation of Gray Code
Starting with 0000 only 1 bit can be changed
0000 0001
Now with 0001 only 1 bit can be changed
If we change 1 than we get 0000 which is
already present so we will change 0001 to 0011
Similarly with 0011 we change one bit 0010 and
it is not present.
Similarly with other numbers.
193. Binary to Gray conversion
• The Most Significant Bit (MSB) of the gray
code is always equal to the MSB of the given
binary code.
• Other bits of the output gray code can be
obtained by XORing binary code bit at that
index and previous index.
194.
195. Gray to binary conversion
• The Most Significant Bit (MSB) of the binary
code is always equal to the MSB of the given
gray code.
• Other bits of the output binary code can be
obtained by checking gray code bit at that
index.
• If current gray code bit is 0, then copy
previous binary code bit, else copy invert of
previous binary code bit