Boolean Algebra and Logic Gates:
Introduction, Logic (AND OR NOT), Boolean theorems, Boolean
Laws, De Morgan’s Theorem, Perfect Induction, Reduction of Logic
expression using Boolean Algebra, Deriving Boolean expression from
given circuit, exclusive OR and Exclusive NOR gates, Universal Logic
gates, Implementation of other gates using universal gates, Input
bubbled logic, Assertion level.
FYBSC IT Digital Electronics Unit I Chapter I Number System and Binary Arithm...Arti Parab Academics
Number System:
Analog System, digital system, numbering system, binary number
system, octal number system, hexadecimal number system, conversion
from one number system to another, floating point numbers, weighted
codes binary coded decimal, non-weighted codes Excess – 3 code, Gray
code, Alphanumeric codes – ASCII Code, EBCDIC, ISCII Code,
Hollerith Code, Morse Code, Teletypewriter (TTY), Error detection
and correction, Universal Product Code, Code conversion.
FYBSC IT Digital Electronics Unit I Chapter II Number System and Binary Arith...Arti Parab Academics
Binary Arithmetic:
Binary addition, Binary subtraction, Negative number representation,
Subtraction using 1’s complement and 2’s complement, Binary
multiplication and division, Arithmetic in octal number system,
Arithmetic in hexadecimal number system, BCD and Excess – 3
arithmetic.
This document discusses various coding schemes including:
- Binary coded decimal (BCD) which assigns a weight to each digit position to represent decimal numbers. Other positively weighted codes and negatively weighted codes are also discussed.
- Gray code which minimizes the number of bit changes between adjacent values represented. This is useful for applications like thumbwheels.
- Character encoding standards like ASCII, EBCDIC, and Unicode which can represent larger character sets with more bits per character.
- Floating point number representation with sign, exponent and mantissa fields.
This document provides an overview of Boolean algebra and logic gates. It begins with reviewing binary number systems, binary arithmetic, and binary codes. It then covers Boolean algebra, truth tables, canonical and standard forms. It also discusses logic operations and logic gates like Karnaugh maps up to 6 variables including don't care conditions. Finally, it discusses sum of products and products of sum representations.
This document discusses binary coded decimal (BCD). It defines BCD as a numerical code that assigns a 4-bit binary code to each decimal digit from 0 to 9. Numbers larger than 9 are expressed digit by digit in BCD. BCD is used because it is easy to encode/decode decimals and useful for digital systems that display decimal outputs. The document also describes how addition and subtraction are performed in BCD through binary addition rules and handling carries.
This document discusses different number systems used in digital techniques. It defines analog and digital signals, with analog having continuous values and digital having a finite set of discrete values. Four main number systems are covered: decimal with base 10, binary with base 2, octal with base 8, and hexadecimal with base 16. Each system's base, symbols used, examples of representations, and how place values determine a number's value are explained. The document aims to introduce students to number systems and their applications in digital contexts.
Binary addition, Binary subtraction, Negative number representation, Subtraction using 1’s complement and 2’s complement, Binary multiplication and division, Arithmetic in octal, hexadecimal number system, BCD and Excess – 3 arithmetic
FYBSC IT Digital Electronics Unit I Chapter I Number System and Binary Arithm...Arti Parab Academics
Number System:
Analog System, digital system, numbering system, binary number
system, octal number system, hexadecimal number system, conversion
from one number system to another, floating point numbers, weighted
codes binary coded decimal, non-weighted codes Excess – 3 code, Gray
code, Alphanumeric codes – ASCII Code, EBCDIC, ISCII Code,
Hollerith Code, Morse Code, Teletypewriter (TTY), Error detection
and correction, Universal Product Code, Code conversion.
FYBSC IT Digital Electronics Unit I Chapter II Number System and Binary Arith...Arti Parab Academics
Binary Arithmetic:
Binary addition, Binary subtraction, Negative number representation,
Subtraction using 1’s complement and 2’s complement, Binary
multiplication and division, Arithmetic in octal number system,
Arithmetic in hexadecimal number system, BCD and Excess – 3
arithmetic.
This document discusses various coding schemes including:
- Binary coded decimal (BCD) which assigns a weight to each digit position to represent decimal numbers. Other positively weighted codes and negatively weighted codes are also discussed.
- Gray code which minimizes the number of bit changes between adjacent values represented. This is useful for applications like thumbwheels.
- Character encoding standards like ASCII, EBCDIC, and Unicode which can represent larger character sets with more bits per character.
- Floating point number representation with sign, exponent and mantissa fields.
This document provides an overview of Boolean algebra and logic gates. It begins with reviewing binary number systems, binary arithmetic, and binary codes. It then covers Boolean algebra, truth tables, canonical and standard forms. It also discusses logic operations and logic gates like Karnaugh maps up to 6 variables including don't care conditions. Finally, it discusses sum of products and products of sum representations.
This document discusses binary coded decimal (BCD). It defines BCD as a numerical code that assigns a 4-bit binary code to each decimal digit from 0 to 9. Numbers larger than 9 are expressed digit by digit in BCD. BCD is used because it is easy to encode/decode decimals and useful for digital systems that display decimal outputs. The document also describes how addition and subtraction are performed in BCD through binary addition rules and handling carries.
This document discusses different number systems used in digital techniques. It defines analog and digital signals, with analog having continuous values and digital having a finite set of discrete values. Four main number systems are covered: decimal with base 10, binary with base 2, octal with base 8, and hexadecimal with base 16. Each system's base, symbols used, examples of representations, and how place values determine a number's value are explained. The document aims to introduce students to number systems and their applications in digital contexts.
Binary addition, Binary subtraction, Negative number representation, Subtraction using 1’s complement and 2’s complement, Binary multiplication and division, Arithmetic in octal, hexadecimal number system, BCD and Excess – 3 arithmetic
This document discusses different types of codes used to encode information for transmission and storage. It begins by explaining that encoding is required to send information unambiguously over long distances and that decoding is needed to retrieve the original information. It then provides reasons for using coding, such as increasing transmission efficiency and enabling error correction. The document proceeds to describe binary coding and how increasing the number of bits allows more items to be uniquely represented. It also discusses properties of good codes like ease of use and error detection. Specific code types are then outlined, including binary coded decimal codes, unit distance codes, error detection codes, and alphanumeric codes. Gray code and excess-3 code are explained as examples.
Fixed-point and floating-point numbers can be represented in computers using binary numbers. Floating-point numbers represent numbers in scientific notation with a sign, mantissa, and exponent. In 8-bit floating point, numbers use 1 bit for sign, 3 bits for exponent, and 4 bits for mantissa, such as 0.001 x 21 = 2.25. Larger precision formats such as 32-bit and 64-bit floating point according to the IEEE standard use more bits for exponent and mantissa.
FYBSC IT Digital Electronics Unit II Chapter II Minterm, Maxterm and Karnaugh...Arti Parab Academics
Minterm, Maxterm and Karnaugh Maps:
Introduction, minterms and sum of minterm form, maxterm and Product
of maxterm form, Reduction technique using Karnaugh maps –
2/3/4/5/6 variable K-maps, Grouping of variables in K-maps, K-maps
for product of sum form, minimize Boolean expression using K-map
and obtain K-map from Boolean expression, Quine Mc Cluskey
Method.
The document discusses binary arithmetic operations including addition, subtraction, multiplication, and division. It provides examples and step-by-step explanations of how to perform each operation in binary. For addition and subtraction, it explains the rules and concepts like carry bits and two's complement. For multiplication, it describes the shift-and-add method. And for division, it outlines the long division approach of shift-and-subtract in binary.
An encoder is a device, circuit, or program that converts information from one format to another. It accepts one or more inputs and generates a multibit output code. The purposes of encoders include standardization, speed, secrecy, security, and reducing size. There are different types of encoders such as simple encoders, priority encoders, and decimal to binary code encoders. Decoders perform the reverse function of converting a code back into a recognizable number or character.
The document discusses different number systems used in computing like binary, decimal, octal and hexadecimal. It explains that computers use the binary number system and each system has a base and set of digits. Decimal uses base 10 with 0-9 digits. Binary uses base 2 with 0-1 digits. Octal uses base 8 with 0-7 digits. Hexadecimal uses base 16 with 0-9 and A-F digits. It also provides examples of how to convert between decimal and these other number systems.
Binary arithmetic is essential for digital computers and systems. It includes four rules for binary addition and subtraction. Binary addition examples show that adding two 1s results in a 1 in the next column with a carry of 1. Binary subtraction uses borrowing to subtract binary numbers, as shown through several examples.
The document discusses the binary number system and how to convert between binary, decimal, octal, and hexadecimal numbers. It also covers binary-coded decimal (BCD). The binary system uses only two digits, 0 and 1. To convert a decimal number to binary, you divide the decimal by 2 and write down the remainders in reverse order. Octal and hexadecimal break binary down into groups of 3 and 4 digits respectively to make large binary numbers easier to read and enter. BCD represents each decimal digit with a 4-bit code to allow easy conversion between decimal and binary.
The document discusses different number systems including binary, decimal, octal, and hexadecimal. It provides details on how to convert between these number systems, including how to convert fractional numbers between bases. Conversion methods covered include dividing numbers into place values to determine the digit values in the target base. The document also discusses representing negative numbers using 1's complement notation.
The document discusses floating point numbers and the IEEE 754 standard. It describes how floating point numbers represent numbers with fractions using a sign bit, exponent field, and fraction field. The IEEE 754 standard uses a biased exponent representation for normalized floating point values, along with special values like infinity and NaN. It also details denormalized numbers, which allow gradual underflow to zero.
This document discusses floating point number representation in IEEE-754 format. It explains that floating point numbers consist of a sign bit, exponent, and mantissa. It describes single and double precision formats, which use excess-127 and excess-1023 exponent biases respectively. Examples are given of representing sample numbers in both implicit and explicit normalized forms using single and double precision formats.
The document discusses decimal and hexadecimal number systems. The decimal system uses 10 symbols (0-9) in a positional notation where the value of each digit depends on its position. Hexadecimal uses 16 symbols (0-9 plus A-F) with a base of 16. To convert between number systems, the integer and fractional parts are converted separately by repeated division or multiplication by the new base. For example, to convert decimal 765.245 to hexadecimal, 765 divides into 16 with remainder 13 and fractional part 0.245 is multiplied by 16 repeatedly.
Binary arithmetic is essential for digital computers and systems. It involves adding, subtracting, multiplying, and dividing binary numbers using basic rules. Signed binary numbers represent positive and negative values using sign-magnitude, 1's complement, and 2's complement methods. Arithmetic operations on signed binary numbers follow rules for handling the sign bit and complement representations.
This document provides an overview of different number systems, including positional and non-positional systems. It describes the binary, decimal, octal, and hexadecimal systems, explaining their bases and symbols. Methods are presented for converting between these systems, such as using binary as an intermediary. Conversions include changing number values, as well as fractional representations. The objective is to understand number systems and perform conversions between binary, octal, decimal, and hexadecimal formats.
The document discusses the binary number system. It begins by defining number systems and the decimal system. It then introduces the binary number system which has a base of 2 and uses only the digits 0 and 1. It shows how to write binary numbers and provides a table to demonstrate counting and place values in the binary system. The document explains two methods for converting between decimal and binary numbers - the division method to convert decimals to binary, and the expansion method to convert binary to decimal. It includes examples and practice problems for students to convert numbers between the two number systems.
This document discusses binary numbers and arithmetic operations on binary numbers. It begins with an introduction to binary numbers, defining them as a numbering system with a base of 2 that uses only the digits 0 and 1. It then explains how addition, subtraction, multiplication, and division are performed on binary numbers, providing examples of each operation. The key methods of binary arithmetic are performing column-by-column addition and subtraction as in decimal, and using bit-wise logic for multiplication and division. Complements are also introduced for simplifying subtraction. In the end, it notes that the binary system has a long history of use prior to its modern application in computers.
Digital Electronics- Number systems & codes VandanaPagar1
This document covers number systems including decimal, binary, hexadecimal and their representations. It discusses how to convert between different number bases including binary to decimal and hexadecimal to decimal. Binary operations like addition, subtraction and codes like binary coded decimal are explained. Non-weighted codes such as gray code are also introduced. Reference books on digital electronics and number systems are provided.
1. Subtraction can be performed using addition by taking the complement of the subtrahend and adding it to the minuend.
2. The 1's complement of a binary number is obtained by flipping all bits, and 1's complement subtraction involves taking the complement of the smaller number and adding it to the larger number.
3. The 2's complement is obtained by adding 1 to the 1's complement, and 2's complement subtraction discards any carry when adding the 2's complement of the smaller number to the larger number.
- Decimal, binary, octal, and hexadecimal are different number systems used to represent numeric values.
- Decimal uses 10 digits (0-9), binary uses two digits (0-1), octal uses 8 digits (0-7), and hexadecimal uses 16 digits (0-9 and A-F).
- Each system has a base or radix - the number of unique digits used. Decimal is base 10, binary base 2, octal base 8, and hexadecimal base 16.
- Numbers can be converted between these systems using division and multiplication operations that take into account the place value of each digit based on the system's base.
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
This document discusses 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.
This document discusses different types of codes used to encode information for transmission and storage. It begins by explaining that encoding is required to send information unambiguously over long distances and that decoding is needed to retrieve the original information. It then provides reasons for using coding, such as increasing transmission efficiency and enabling error correction. The document proceeds to describe binary coding and how increasing the number of bits allows more items to be uniquely represented. It also discusses properties of good codes like ease of use and error detection. Specific code types are then outlined, including binary coded decimal codes, unit distance codes, error detection codes, and alphanumeric codes. Gray code and excess-3 code are explained as examples.
Fixed-point and floating-point numbers can be represented in computers using binary numbers. Floating-point numbers represent numbers in scientific notation with a sign, mantissa, and exponent. In 8-bit floating point, numbers use 1 bit for sign, 3 bits for exponent, and 4 bits for mantissa, such as 0.001 x 21 = 2.25. Larger precision formats such as 32-bit and 64-bit floating point according to the IEEE standard use more bits for exponent and mantissa.
FYBSC IT Digital Electronics Unit II Chapter II Minterm, Maxterm and Karnaugh...Arti Parab Academics
Minterm, Maxterm and Karnaugh Maps:
Introduction, minterms and sum of minterm form, maxterm and Product
of maxterm form, Reduction technique using Karnaugh maps –
2/3/4/5/6 variable K-maps, Grouping of variables in K-maps, K-maps
for product of sum form, minimize Boolean expression using K-map
and obtain K-map from Boolean expression, Quine Mc Cluskey
Method.
The document discusses binary arithmetic operations including addition, subtraction, multiplication, and division. It provides examples and step-by-step explanations of how to perform each operation in binary. For addition and subtraction, it explains the rules and concepts like carry bits and two's complement. For multiplication, it describes the shift-and-add method. And for division, it outlines the long division approach of shift-and-subtract in binary.
An encoder is a device, circuit, or program that converts information from one format to another. It accepts one or more inputs and generates a multibit output code. The purposes of encoders include standardization, speed, secrecy, security, and reducing size. There are different types of encoders such as simple encoders, priority encoders, and decimal to binary code encoders. Decoders perform the reverse function of converting a code back into a recognizable number or character.
The document discusses different number systems used in computing like binary, decimal, octal and hexadecimal. It explains that computers use the binary number system and each system has a base and set of digits. Decimal uses base 10 with 0-9 digits. Binary uses base 2 with 0-1 digits. Octal uses base 8 with 0-7 digits. Hexadecimal uses base 16 with 0-9 and A-F digits. It also provides examples of how to convert between decimal and these other number systems.
Binary arithmetic is essential for digital computers and systems. It includes four rules for binary addition and subtraction. Binary addition examples show that adding two 1s results in a 1 in the next column with a carry of 1. Binary subtraction uses borrowing to subtract binary numbers, as shown through several examples.
The document discusses the binary number system and how to convert between binary, decimal, octal, and hexadecimal numbers. It also covers binary-coded decimal (BCD). The binary system uses only two digits, 0 and 1. To convert a decimal number to binary, you divide the decimal by 2 and write down the remainders in reverse order. Octal and hexadecimal break binary down into groups of 3 and 4 digits respectively to make large binary numbers easier to read and enter. BCD represents each decimal digit with a 4-bit code to allow easy conversion between decimal and binary.
The document discusses different number systems including binary, decimal, octal, and hexadecimal. It provides details on how to convert between these number systems, including how to convert fractional numbers between bases. Conversion methods covered include dividing numbers into place values to determine the digit values in the target base. The document also discusses representing negative numbers using 1's complement notation.
The document discusses floating point numbers and the IEEE 754 standard. It describes how floating point numbers represent numbers with fractions using a sign bit, exponent field, and fraction field. The IEEE 754 standard uses a biased exponent representation for normalized floating point values, along with special values like infinity and NaN. It also details denormalized numbers, which allow gradual underflow to zero.
This document discusses floating point number representation in IEEE-754 format. It explains that floating point numbers consist of a sign bit, exponent, and mantissa. It describes single and double precision formats, which use excess-127 and excess-1023 exponent biases respectively. Examples are given of representing sample numbers in both implicit and explicit normalized forms using single and double precision formats.
The document discusses decimal and hexadecimal number systems. The decimal system uses 10 symbols (0-9) in a positional notation where the value of each digit depends on its position. Hexadecimal uses 16 symbols (0-9 plus A-F) with a base of 16. To convert between number systems, the integer and fractional parts are converted separately by repeated division or multiplication by the new base. For example, to convert decimal 765.245 to hexadecimal, 765 divides into 16 with remainder 13 and fractional part 0.245 is multiplied by 16 repeatedly.
Binary arithmetic is essential for digital computers and systems. It involves adding, subtracting, multiplying, and dividing binary numbers using basic rules. Signed binary numbers represent positive and negative values using sign-magnitude, 1's complement, and 2's complement methods. Arithmetic operations on signed binary numbers follow rules for handling the sign bit and complement representations.
This document provides an overview of different number systems, including positional and non-positional systems. It describes the binary, decimal, octal, and hexadecimal systems, explaining their bases and symbols. Methods are presented for converting between these systems, such as using binary as an intermediary. Conversions include changing number values, as well as fractional representations. The objective is to understand number systems and perform conversions between binary, octal, decimal, and hexadecimal formats.
The document discusses the binary number system. It begins by defining number systems and the decimal system. It then introduces the binary number system which has a base of 2 and uses only the digits 0 and 1. It shows how to write binary numbers and provides a table to demonstrate counting and place values in the binary system. The document explains two methods for converting between decimal and binary numbers - the division method to convert decimals to binary, and the expansion method to convert binary to decimal. It includes examples and practice problems for students to convert numbers between the two number systems.
This document discusses binary numbers and arithmetic operations on binary numbers. It begins with an introduction to binary numbers, defining them as a numbering system with a base of 2 that uses only the digits 0 and 1. It then explains how addition, subtraction, multiplication, and division are performed on binary numbers, providing examples of each operation. The key methods of binary arithmetic are performing column-by-column addition and subtraction as in decimal, and using bit-wise logic for multiplication and division. Complements are also introduced for simplifying subtraction. In the end, it notes that the binary system has a long history of use prior to its modern application in computers.
Digital Electronics- Number systems & codes VandanaPagar1
This document covers number systems including decimal, binary, hexadecimal and their representations. It discusses how to convert between different number bases including binary to decimal and hexadecimal to decimal. Binary operations like addition, subtraction and codes like binary coded decimal are explained. Non-weighted codes such as gray code are also introduced. Reference books on digital electronics and number systems are provided.
1. Subtraction can be performed using addition by taking the complement of the subtrahend and adding it to the minuend.
2. The 1's complement of a binary number is obtained by flipping all bits, and 1's complement subtraction involves taking the complement of the smaller number and adding it to the larger number.
3. The 2's complement is obtained by adding 1 to the 1's complement, and 2's complement subtraction discards any carry when adding the 2's complement of the smaller number to the larger number.
- Decimal, binary, octal, and hexadecimal are different number systems used to represent numeric values.
- Decimal uses 10 digits (0-9), binary uses two digits (0-1), octal uses 8 digits (0-7), and hexadecimal uses 16 digits (0-9 and A-F).
- Each system has a base or radix - the number of unique digits used. Decimal is base 10, binary base 2, octal base 8, and hexadecimal base 16.
- Numbers can be converted between these systems using division and multiplication operations that take into account the place value of each digit based on the system's base.
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
This document discusses 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.
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.
This document provides an overview of logic circuits and their components. It introduces basic logic gates like AND, OR, NAND, and NOR gates. It explains how these gates can be combined to build more complex logic circuits and discusses different types of logic circuits like bistables and flip-flops. It also covers integrated circuit logic devices and different scales of integration.
boolean algrebra and logic gates in shortRojin Khadka
The document discusses logic gates and Boolean algebra. It describes the basic logic gates - OR, AND, NOT, NAND, NOR and XOR gates. It explains their symbols, truth tables and functions. Logic gates are electronic circuits that make logic decisions. Boolean algebra uses values of 0 and 1 instead of numbers. It has laws like commutative, associative and distributive laws that define operations on logic values. Logic gates and Boolean algebra are important for designing digital circuits and simplifying logical functions.
The document discusses basic and derived logic gates. It begins by introducing Boolean algebra and defining logic 0 and 1. It then explains the three basic logic gates - OR, AND, and NOT - through truth tables and circuit diagrams. The OR gate's output is 1 if any input is 1. The AND gate's output is 1 only if all inputs are 1. The NOT gate inverts the input. Complex logic circuits can be described algebraically using these basic gates and Boolean operations.
The document discusses different digital logic components including logic gates, flip flops, registers, and counters. It describes the basic types of logic gates such as AND, OR, NOT, NAND, and NOR gates. It also discusses different types of flip flops including T, S-R, J-K, and D flip flops which are used to store binary data. Registers are formed using groups of flip flops to store multi-bit data. Counters are also discussed as another component of digital logic systems.
This document provides an overview of digital electronics and electronic principles. It covers topics such as number systems, binary codes, Boolean algebra, logic gates, and applications of digital circuits. Number systems and conversions between binary, decimal, octal, and hexadecimal are examined. Boolean algebra and logic gates like AND, OR, NOT, NAND, and NOR are described along with their truth tables. Combinational logic circuits including adders, multiplexers, and decoders are discussed. Sequential logic and memory elements like latches and flip-flops are also introduced. The document provides fundamental information on digital electronics and serves as an introduction to the key concepts and components in the field.
The document provides an introduction to logic gates and Boolean algebra. It discusses the different types of logic gates including NOT, AND, OR, NAND, NOR, XOR, and XNOR gates. Truth tables and logic circuit diagrams are presented as ways to represent the working of logic circuits. Boolean algebra rules are introduced as a way to simplify logic expressions without changing their functionality. Examples of Boolean algebra rules and their applications are also provided.
Digital logic is based on the binary number system of 0s and 1s. This two-valued logic system allows statements to be either true or false. One reason for using binary is that electronic circuits can be designed to reliably represent and switch between two states. There are two classes of digital logic - combinational logic, where outputs depend only on current inputs, and sequential logic, where outputs also depend on prior states. Basic logic gates like AND, OR, and NOT are used to combine input signals in circuits. The Karnaugh map provides a visual method to simplify Boolean logic expressions by grouping adjacent ones to minimize variables.
This document presents a presentation on logic gates such as OR, AND, and NOT gates. It begins with an introduction to logic gates and Boolean algebra. It then describes the basic OR, AND, and NOT gates. The presentation continues by explaining some other gates like NAND, NOR, XOR and XNOR gates. It provides an example of combining gates. Finally, it proposes a real-world problem of designing a car circuit to sound a buzzer based on speed or seatbelt use and shows the logic gate implementation of the solution.
M. FLORENCE DAYANA/unit - II logic gates and circuits.pdfDr.Florence Dayana
Logic Gates, Truth Table, AND Gate
Types of Digital Logic AND Gate, The 2-input and 3-input AND Gate, OR Gate, Types of Digital Logic AND Gate, The 2-input OR gate, The 3-input OR gate, NOT Gate, NAND Gate, The 2-input NAND Gate, The 3-input NAND Gate, NOR Gate, 2-input NOR gate
Just like other gates, XOR gate or Exclusive-OR gate
This document discusses logic gates, including their introduction, types, truth tables, and applications. It describes the basic AND, OR, NOT, NAND, and NOR gates and provides their truth tables. Logic gates are elementary building blocks of digital circuits that have binary inputs and outputs. They are used to build circuits for applications like burglar alarms and fire alarms.
The document discusses various logic gates like OR, AND, and NOT gates. It defines what each gate is, provides their truth tables and Boolean expressions, and includes examples of simple circuits to realize each gate using common electronic components like switches and bulbs. The document also acknowledges the sources used and provides an introduction, theory, and working of the OR, AND, and NOT gates along with the aim, components, theory, and working of sample circuits to demonstrate each gate.
Boolean Aljabra.pptx of dld and computeritxminahil29
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This document provides an introduction to computer systems and digital logic design. It discusses binary logic, logic gates like AND, OR, NOT, NAND and NOR gates. It describes how logic gates can be used to implement Boolean logic and algorithms. The document also covers topics like Boolean algebra, digital circuits, binary coded decimal, ASCII character set and references. The overall purpose is to introduce concepts related to computer systems and digital logic.
This document provides an overview of digital electronics and Boolean algebra topics, including:
- Boolean algebra deals with binary variables and logical operations. It originated from George Boole's 1854 book.
- Logic gates are basic building blocks of digital systems. Common logic gates include AND, OR, NOT, NAND, NOR gates.
- Boolean laws like commutative, associative, distributive, De Morgan's theorems are used to simplify logic expressions.
- Karnaugh maps are used to minimize logic expressions into sum of products or product of sums form. Don't care conditions allow for further simplification.
- Universal gates like NAND and NOR can be used to construct all other logic gates
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.
Boolean algebra deals with logical operations on binary variables that have two possible values, typically represented as 1 and 0. George Boole first introduced Boolean algebra in 1854. Boolean algebra uses logic gates like AND, OR, and NOT as basic building blocks. Positive logic represents 1 as high and 0 as low, while negative logic uses the opposite. Boolean algebra laws and Karnaugh maps are used to simplify logical expressions. Don't care conditions allow for groupings in K-maps that further reduce expressions.
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Computer Hardware: Central Processing Unit (CPU), memory (RAM and ROM), input and output devices, storage devices.
Computer Software: Operating systems, application software, programming languages. Computer Applications in psychology
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Computer Hardware: Central Processing Unit (CPU), memory (RAM and ROM), input and output devices, storage devices.
Computer Software: Operating systems, application software, programming languages. Computer Applications in Healthcare
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Internet and World Wide Web: Understanding the Internet, web browsers, search engines, online research techniques.
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
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বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
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This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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9
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Azure Interview Questions and Answers PDF By ScholarHat
FYBSC IT Digital Electronics Unit II Chapter I Boolean Algebra and Logic Gates
1. BOOLEAN ALGEBRA
AND LOGIC GATES
&
MINTERM, MAXTERM
AND KARNAUGH
MAPS
UNIT II
DIGITAL
ELECTRONICS
PROF.ARTI GAVAS-PARAB
ANNA LEELA COLLEGE OF COMMERCE AND ECONOMICS,SHOBHA
JAYARAM SHETTY COLLEGE FOR BMS
CHAPTER I
2. UNIT II: CONTENTS
BooleanAlgebra and Logic Gates:
Introduction, Logic (AND OR NOT),
Boolean theorems,Boolean Laws, De Morgan’sTheorem,
Perfect Induction,Reduction of Logic expression using Boolean Algebra,
Deriving Boolean expression from given circuit, exclusive OR and Exclusive NOR gates,
Universal Logic gates, Implementation of other gates using universal gates, Input bubbled logic,Assertion level.
Minterm, Maxterm and Karnaugh Maps:
Introduction, minterms and sum of minterm form, maxterm and Product of maxterm form,
Reduction technique using Karnaugh maps – 2/3/4/5/6 variable K-maps,Grouping of variables in K-maps,K-maps for product
of sum form,
Mminimize Boolean expression using K-map and obtain K-map from Boolean expression,
Quine Mc Cluskey Method.
C
H
A
P
T
E
R
I
C
H
A
P
T
E
R
II
3. BOOLEAN ALGEBRA AND LOGIC GATES
Boolean Algebra is the mathematical foundation of digital circuits.
Boolean Algebra specifies the relationship between Boolean variables which is used to design combinational logic circuits
using Logic Gates.
The truth table shows a logic circuit's output response to all of the input combinations.
Boolean Algebra
A BooleanVariable takes the value of either 0 (False) or 1 (True).
Symbols are used to represent Boolean variables e.g.A, B, C,X,Y, Z
There are three basic logic operationsAND, OR,NOT
The Boolean Operators are • + ‾
A + B means A OR B
A • B means A AND B
A means NOT A
Nodes in a circuit are represented by BooleanVariables
The most practical use of Boolean algebra is to simplify Boolean expressions which means less logic gates are used to
implement the combinational logic circuit.
4. LOGIC GATES
Logic gates are electronic circuits that implement the basic functions of Boolean Algebra.There is a symbol for each gate.
Logic levels (0 or 1) are represented by means of a voltage level.
High voltage (5V,3.3V,2.5V, etc.) is 1
Low voltage (0V) is 0
The table used to represent the boolean expression of a logic gate function is commonly called a TruthTable. A logic
gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon
the combination of these input(s).
There are “four” possible input combinations or 22 of “OFF” and “ON” for the two inputs.
Then the four possible combinations of A and B for a 2-input logic gate is given as:
Input Combination 1. – “OFF” – “OFF” or ( 0, 0 )
Input Combination 2. – “OFF” – “ON” or ( 0, 1 )
Input Combination 3. – “ON” – “OFF” or ( 1, 0 )
Input Combination 4. – “ON” – “ON” or ( 1, 1 )
Therefore, a 3-input logic circuit would have 8 possible input combinations or 23 and a 4-input logic circuit would have 16
or 24, and so on as the number of inputs increases.Then a logic circuit with “n” number of inputs would have 2n possible
input combinations of both “OFF” and “ON”.
6. 2-INPUT OR (INCLUSIVE OR) GATE
For a 2-input OR gate, the output Q is true if EITHER input A “OR” input B is true, giving the Boolean Expression
of: ( Q = A or B ).
Symbol TruthTable
A B Q
0 0 0
0 1 1
1 0 1
1 1 1
Boolean Expression Q = A+B Read as A OR B gives Q
7. 2-INPUT AND GATE
For a 2-input AND gate, the output Q is true if BOTH input A “AND” input B are both true, giving the Boolean
Expression of: ( Q = A and B ).
Symbol TruthTable
A B Q
0 0 0
0 1 0
1 0 0
1 1 1
Boolean Expression Q = A.B Read as A AND B gives Q
8. NOT GATE (INVERTER)
For a single input NOT gate, the output Q is ONLY true when the input is “NOT” true, the output is the inverse
or complement of the input giving the Boolean Expression of: ( Q = NOT A ).
Symbol TruthTable
A Q
0 1
1 0
Boolean Expression Q = NOT A or A Read as inversion of A gives Q
9. 2-INPUT NAND (NOT AND) GATE
For a 2-input NAND gate, the output Q is NOT true if BOTH input A and input B are true, giving the Boolean
Expression of: ( Q = not(A AND B) ).
Symbol TruthTable
A B Q
0 0 1
0 1 1
1 0 1
1 1 0
Boolean Expression Q = A .B Read as A AND B gives NOT-Q
10. 2-INPUT NOR (NOT OR) GATE
For a 2-input NOR gate, the output Q is true if BOTH input A and input B are NOT true, giving the Boolean
Expression of: ( Q = not(A OR B) ).
Symbol TruthTable
A B Q
0 0 1
0 1 0
1 0 0
1 1 0
Boolean Expression Q = A+B Read as A OR B gives NOT-Q
11. 2-INPUT EX-OR (EXCLUSIVE OR) GATE
Along with standard logic gates there are also two special types of logic gate function called an Exclusive-OR Gate and an Exclusive-
NOR Gate.
The Boolean expression to indicate an Exclusive-OR or Exclusive-NOR function is to a symbol with a plus sign inside a circle,( ⊕ ).
For a 2-input Ex-OR gate, the output Q is true if EITHER inputA or if input B is true,but NOT both giving the Boolean Expression of:
( Q = (A and NOT B) or (NOT A and B) ).
Symbol TruthTable
A B Q
0 0 0
0 1 1
1 0 1
1 1 0
Boolean Expression Q = A ⊕ B
12. 2-INPUT EX-NOR (EXCLUSIVE NOR) GATE
For a 2-input Ex-NOR gate, the output Q is true if BOTH input A and input B are the same, either true or false,
giving the Boolean Expression of: ( Q = (A and B) or (NOT A and NOT B) ).
Symbol TruthTable
A B Q
0 0 1
0 1 0
1 0 0
1 1 1
Boolean Expression Q = A ⊕ B
13. SUMMARY OF 2-INPUT LOGIC GATES
Inputs TruthTable Outputs For Each Gate
A B AND NAND OR NOR EX-OR EX-NOR
0 0 0 1 0 1 0 1
0 1 0 1 1 0 1 0
1 0 0 1 1 0 1 0
1 1 1 0 1 0 0 1
Logic Function Boolean Notation
AND A.B
OR A+B
NOT A
NAND A .B
NOR A+B
EX-OR (A.B) + (A.B) or A ⊕ B
EX-NOR (A.B) + (A.B) or A ⊕ B
The following table gives a list of the
common logic functions and their equivalent
Boolean notation.
The following TruthTable compares the logical functions of the 2-
input logic gates discussed.
There are many more logic gates with 3, 4 even 8
individual inputs.The multiple input gates are no
different to the simple 2-input gates above, So a 4-
input AND gate would still require ALL 4-inputs to
be present to produce the required output at Q
and its larger truth table would reflect that.
14. BOOLEANTHEOREMS
Boolean theorems and laws are used to simplify the various logical expressions.
In a digital designing problem, a unique logical expression is evolved from the truth table.
If this logical expression is simplified the designing becomes easier.
The Boolean algebra is mainly used in digital electronics, set theory and digital electronics.
It is also used in all modern programming languages.
There are few basic laws and theorems of Boolean algebra, some of which are familiar to everyone such as
Cumulative Law,
Associative Law,
Distributive law,
DeMorgan’sTheorems,
Double Inversion law and
DualityTheorems.
15. BOOLEANTHEOREMS
The Cumulative Law
The below two equations are based on the fact that
the output of an OR or AND gate remains
unaffected while the inputs are exchanged
themselves.
The equation of the cumulative law is given below.
The Associative Law
The equation is given as
These laws illustrate that the order of combining
input variables has no effect on the final answer.
16. BOOLEANTHEOREMS
The Distributive Law
The equation is given below.
Double Inversion Law
The equation is given as
The law states that the double complement
(complement of the complement) of a variable
equals the variable itself.
17. BOOLEANTHEOREMS
The Identity Law (OR)
basic identities of OR operations:
The authentication of the above all
equations can be checked by substituting
the value of A = 0 or A = 1.
The Identity Law (AND)
basic identities of AND operations:
One can check the validity of the above
identities by substituting the value of A= 0
or A = 1.
18. BOOLEANTHEOREMS
The DeMorgan’s theorem
The equations are given below.
The equation (6) says that a NOR gate is
equivalent to a bubbled AND gate, and the
equation (7) says that NAND gate is
equivalent to a bubbled OR gate.
DualityTheorems
The new Boolean relation can be derived with the help of Duality
theorem.According to this theorem for the given Boolean
relation,the new Boolean relation can be derived by the
following steps.
Changing each OR sign to an AND sign.
Changing eachAND sign to an OR sign.
Complementing each 0 or 1 appearing in the given Boolean identity.
For example:
The distributive law states that
Now, by using the duality theorem, we can get the new relation by
interchanging each OR and AND sign.The equation (8) becomes.
The equation (9) is a new Boolean relation. Similarly,for any other
Boolean relation,its dual relation can also be derived.
19. DEMORGAN’STHEOREM
DeMorgan’sTheorem is mainly used to solve the various Boolean algebra expressions.
The Demorgan’s theorem defines the uniformity between the gate with same inverted input and output.
It is used for implementing the basic gate operation likes NAND gate and NOR gate.
The Demorgan’s theorem mostly used in digital programming and for making digital circuit diagrams.
There are two DeMorgan’s Theorems.
DeMorgan’s FirstTheorem
DeMorgan’s SecondTheorem
DeMorgan’s first theorem states that two (or more) variables NOR´ed together is the same as the two variables
inverted (Complement) and AND´ed, while the second theorem states that two (or more) variables NAND´ed
together is the same as the two terms inverted (Complement) and OR´ed.
That is replace all the OR operators with AND operators, or all the AND operators with an OR operators.
20. DEMORGAN’S FIRSTTHEOREM
DeMorgan’s First theorem proves that when two (or more) input variables are AND’ed and negated, they are
equivalent to the OR of the complements of the individual variables.Thus the equivalent of the NAND function
and is a negative-OR function proving that A.B = A+B and we can show this using the following table.
Verifying DeMorgan’s First Theorem usingTruthTable
Inputs TruthTable Outputs For EachTerm
B A A.B A.B A B A + B
0 0 0 1 1 1 1
0 1 0 1 0 1 1
1 0 0 1 1 0 1
1 1 1 0 0 0 0
DeMorgan’s First Law Implementation using Logic Gates
We can also show that A.B = A+B using logic gates as shown.
21. DEMORGAN’S SECONDTHEOREM
DeMorgan’s Second theorem proves that when two (or more) input variables are OR’ed and negated, they are
equivalent to the AND of the complements of the individual variables.Thus the equivalent of the NOR function and is a
negative-AND function proving that A+B = A.B and again we can show this using the following truth table.
Verifying DeMorgan’s SecondTheorem usingTruth Table DeMorgan’s Second Law Implementation using Logic Gates
We can also show that A+B = A.B using logic gates as shown.
Inputs TruthTable Outputs For EachTerm
B A A+B A+B A B A . B
0 0 0 1 1 1 1
0 1 1 0 0 1 0
1 0 1 0 1 0 0
1 1 1 0 0 0 0
22. DEMORGAN’STHEOREM
Although we have used DeMorgan’s theorems with only two input variables A and B,
they are equally valid for use with three, four or more input variable expressions,
for example:
For a 3-variable input
A.B.C = A+B+C
and also
A+B+C = A.B.C
For a 4-variable input
A.B.C.D = A+B+C+D
and also
A+B+C+D = A.B.C.D
And so on.
23. PERFECT INDUCTION
Perfect induction, Proof by exhaustion, also
known as proof by cases, or the brute force
method.
It is a method of mathematical proof in which the
statement to be proved is split into a finite number
of cases and each case is checked to see if the
proposition in question holds.
Perfect induction says that if you check the veracity of
a theorem for all possible input combinations, then
the theorem is true in its entirety.
This is, if it is fulfilled in each case, it is fulfilled
in general.
This path can be used in Boolean Algebra since the
variables have only two possible values: 0 and 1, whilst
in our algebra each variable can have infinite values.
For example, to demonstrate the distributed property
of the sum against the product (which is not fulfilled in
common algebra). X+(Y·Z) = (X+Y)·(X+Z)
X Y Z X+(Y·Z) (X+Y)·(X+Z)
0 0 0 0 0
0 0 1 0 0
0 1 0 0 0
0 1 1 1 1
1 0 0 1 1
1 0 1 1 1
1 1 0 1 1
1 1 1 1 1
In the table, all possible values for X,Y and Z, the expressions
X+(Y·Z) and (X+Y)·(X+Z) are identical, and thus, by perfect
induction,both expressions are equivalent.
24. TEN BASIC RULES OF BOOLEAN ALGEBRA
Sr. No. Rule Equation
1 Anything ANDed with a 0 is equal to 0. A * 0 = 0
2 Anything ANDed with a 1 is equal to itself. A * 1 = A
3 Anything ORed with a 0 is equal to itself. A + 0 = A
4 Anything ORed with a 1 is equal to 1. A + 1 = 1
5 Anything ANDed with itself is equal to itself. A * A = A
6 Anything ORed with itself is equal to itself. A + A = A
7 Anything ANDed with its own complement equals 0.
8 Anything ORed with its own complement equals 1.
9 Anything complemented twice is equal to the original.
10 The two variable rule.
25. TEN BASIC RULES OF BOOLEAN ALGEBRA
Boolean
Expression
Boolean Algebra
Law or Rule
A + 1 = 1 Annulment
A + 0 = A Identity
A . 1 = A Identity
A . 0 = 0 Annulment
A + A = A Idempotent
A .A = A Idempotent
NOT A’ = A Double Negation
Boolean
Expression
Boolean Algebra
Law or Rule
A + A’ = 1 Complement
A .A’ = 0 Complement
A+B = B+A Commutative
A.B = B.A Commutative
(A+B)’ = A’.B’ de Morgan’sTheorem
(A.B)’ = A’+B’ de Morgan’sTheorem
26. REDUCTION OF LOGIC EXPRESSION USING BOOLEAN ALGEBRA
Complex combinational logic circuits must be reduced without changing the function of the circuit.
Reduction of a logic circuit means the same logic function with fewer gates and/or inputs.
The first step to reducing a logic circuit is to write the Boolean Equation for the logic function.
The next step is to apply as many rules and laws as possible in order to decrease the number of terms and
variables in the expression.
To apply the rules of Boolean Algebra it is often helpful to first remove any parentheses or brackets.
After removal of the parentheses,common terms or factors may be removed leaving terms that can be reduced
by the rules of Boolean Algebra.
The final step is to draw the logic diagram for the reduced Boolean Expression.
27. SIMPLIFICATION: EXAMPLE 1
Using the above laws, simplify the following expression: (A + B)(A + C)
Q = (A + B).(A + C)
A.A + A.C + A.B + B.C – Distributive law
A + A.C + A.B + B.C – IdempotentAND law (A.A = A)
A(1 + C) + A.B + B.C – Distributive law
A.1 + A.B + B.C – Identity OR law (1 + C = 1)
A(1 + B) + B.C – Distributive law
A.1 + B.C – Identity OR law (1 + B = 1)
Q = A + (B.C) – IdentityAND law (A.1 = A)
Then the expression: (A + B)(A + C) can be simplified to A + (B.C) as in the Distributive law.
Draw Logic Diagram for
previous expression and
simplified expression.
30. DERIVING BOOLEAN EXPRESSION FROM GIVEN CIRCUIT
Sometimes,we need to be able to derive the Boolean
expression of a logic gate diagram.We might want to do
this, for example, so that we can investigate simplifying
the design.We will look at some examples of this now.
Example 1
Consider the following circuit gate diagram:
Next, you need to start on the left and work your way through
each part, working out what the output is after each gate.
After part 1, we haveA.B and A + B
After part 2, we have invertedA.B so we now haveA.B
After part 3, we have put the parts together in an AND gate
from part 2 and have
(A.B)(A + B)
Let's draw out the truth table for this diagram:
31. DERIVING BOOLEAN EXPRESSION FROM GIVEN CIRCUIT: EXAMPLE
Example 2
Consider the following logic gate diagram.
Example 3
It doesn't matter how many inputs you have,or even if
your circuit diagram includes NAND or NOR gates.
Consider the following logic gate diagram.
32. GENERATING SCHEMATIC DIAGRAMS FROM BOOLEAN EXPRESSIONS
Example: B(A + C)
To do this, evaluate the expression, following proper mathematical order
of operations (multiplication before addition, operations inside parentheses
before anything else), and draw gates for each step.
Remember again that OR gates are equivalent to Boolean addition, while
AND gates are equivalent to Boolean multiplication.
In this case, we would begin with the sub-expression “A + C”, which is an
OR gate.
The next step in evaluating the expression “B(A + C)” is to multiply (AND
gate) the signal B by the output of the previous gate (A + C).
Step 1:
Step 2:
33. GENERATING SCHEMATIC DIAGRAMS FROM BOOLEAN EXPRESSIONS: EXAMPLES
Consider the Boolean expression AB+CD.
The corresponding digital logic circuit is:
Other examples:
34. GENERATING SCHEMATIC DIAGRAMS FROM BOOLEAN EXPRESSIONS: HOMEWORK
1. Draw digital logic circuits for these Boolean
expressions:
1. Give the equivalent Boolean expressions for these digital
logic circuits
35. UNIVERSAL LOGIC GATES & IMPLEMENTATION OF OTHER GATES USING UNIVERSAL GATES
They are called as “Universal
Gates” because-
They can realize all the binary
operations.
All the basic logic gates can be
derived from them.
They have the following properties-
Universal gates are not associative
in nature.
Universal gates are commutative in
nature.
There are following two universal
logic gates-
NAND Gate
NOR Gate
1. NAND Gate-
A NAND Gate is constructed by connecting a NOT Gate at the output terminal of
the AND Gate.
The output of NAND gate is high (‘1’) if at least one of its inputs is low (‘0’).
The output of NAND gate is low (‘0’) if all of its inputs are high (‘1’).
2. NOR Gate-
A NOR Gate is constructed by connecting a NOT Gate at the output terminal of the
OR Gate.
The output of OR gate is high (‘1’) if all of its inputs are low (‘0’).
The output of OR gate is low (‘0’) if any of its inputs is high (‘1’).
36. NAND GATE IS A UNIVERSAL GATE
NAND gates can be connected to form any other
logic gates.
Figures 1,2,3 show how NAND gates can be
connected to form INVERTER,AND, and OR
gates.
These gates can be combined to form the other
logic gates according to the symbolic logic
definitions.
37. NAND AS NOR
Input A Input B
Output
Q
0 0 1
0 1 0
1 0 0
1 1 0
TruthTable
38. NAND AS XOR
Input A Input B
Output
Q
0 0 0
0 1 1
1 0 1
1 1 0
TruthTable
39. NAND AS XNOR
Input A Input B
Output
Q
0 0 1
0 1 0
1 0 0
1 1 1
TruthTable
40. NOR GATE IS A UNIVERSAL GATE
NOT gate is made by joining the inputs of a NOR gate.As a
NOR gate is equivalent to an OR gate leading to NOT gate,
this automatically sees to the "OR" part of the NOR gate,
eliminating it from consideration and leaving only the NOT
part.
An OR gate is made by inverting the output of a NOR gate.
Note that we already know that a NOT gate is equivalent to
a NOR gate with its inputs joined.
An AND gate gives a 1 output when both inputs are 1.
Therefore, an AND gate is made by inverting the inputs of a
NOR gate.Again, note that a NOT gate is equivalent to a
NOR with its inputs joined.
41. NOR AS NAND
Input A Input B
Output
Q
0 0 1
0 1 1
1 0 1
1 1 0
TruthTable
42. NOR AS XNOR
Input A Input B
Output
Q
0 0 1
0 1 0
1 0 0
1 1 1
TruthTable
43. NOR AS XOR
Input A Input B
Output
Q
0 0 0
0 1 1
1 0 1
1 1 0
TruthTable
44. INPUT BUBBLED LOGIC:ALTERNATIVE LOGIC GATES
Alternative logic gate is an alternate logic gate that produces the same output as the original logic gate.
and can be used during the unavailability of the original logic gate to serve the same purpose.
Alternative logic gates are also called as Alternate Gates.
Alternative logic gates are also called as Bubbled Gates since they contain bubbles in them.
The following table shows the original logic gate and its corresponding alternate gate
Bubble pushing is a technique to
apply De Morgan's theorem
directly to the logic diagram.
1. Change the logic gate (AND
to OR and OR to AND).
2. Add bubbles to the inputs
and outputs where there
were none, and remove the
original bubbles.
45. ASSERTION LEVEL
Assertion level is the voltage level in a logic circuit that represents a logical "1".
Common level for high = +5v and low = 0v.
A logical AND circuit that operates with assertion high (also called positiveAND) requires high level on all inputs to
yield a high output.
If you change your terms of reference to assertion low, then the exact same circuit becomes an OR - any low input
yields a low output (also called negative OR).
PositiveAND == Negative OR
Assertion in this case simply means in which value is the pin active.
Digital Circuits have 1st High Assertion Logic Level
From theView Point of Gates (Circuit) the Digital Signal PulseTrain has a ZERO (0-0.8V) logic level as a LOW and ONE (approx 2-
5V) Logic level as HIGH
2nd Low Assertion Logic Level
From theView Point of Gates (Circuit) the Digital Signal PulseTrain has a ZERO (0-0.8V) logic level as a HIGH and ONE (approx 2-
5V) Logic level as LOW
Low Assertion Logic level is indicated by a bubble at either input and/or output of a gate.