This document provides information about different types of counters, including asynchronous counters, synchronous counters, MSI counters, and specific counter integrated circuits. It defines counters and describes their basic characteristics. It discusses asynchronous ripple counters and their timing. It provides examples of decade and binary counters. It describes synchronous counters and MSI counters like the 74LS163 4-bit synchronous counter. Finally, it provides truth tables, logic diagrams, and application information for common counter ICs like the 7490, 7492, 7493, and 74LS163.
This document discusses ripple counters and their characteristics:
- Ripple counters have a modulus (MOD) which is the number of states the counter cycles through before repeating. The MOD is equal to 2n where n is the number of flip-flops.
- State transition diagrams graphically represent the sequence of states a counter goes through with each clock pulse.
- Common integrated circuits used for ripple counters include the 74LS90, 74LS92, 74LS93 and 74HC390. The 74LS93 and 74HC390 can be configured to count to different MODs by controlling enable inputs.
- The internal logic of the 74LS93 is shown, with the clock pulse applied to
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
- Boolean algebra uses binary values (1/0) to represent true/false in digital circuits.
- The basic Boolean operations are AND, OR, and NOT. Truth tables and Boolean expressions can both be used to represent the functions of circuits.
- Boolean expressions can be simplified using algebraic rules like commutative, distributive, DeMorgan's, and absorption laws. This allows simpler circuit implementations.
This document provides an overview of digital logic circuits and sequential circuits. It discusses various logic gates like OR, AND, NOT, NAND, NOR and XOR gates. It explains their truth tables and symbols. It also covers Boolean algebra, map simplification using K-maps, combinational circuits like multiplexers, demultiplexers, encoders and decoders. Finally, it describes different types of flip-flops like SR, D, JK and T flip-flops which are used to build sequential circuits that have memory and can store past states.
DIGITAL ELECTRONICS- Logic Gates
The AND gate
The OR gate
The NOT gate (or inverter)
The NAND gate
The NOR gate
The Exclusive OR gate
The Exclusive NOR gate
This document defines and classifies different types of binary codes. It explains that binary codes represent numeric and alphanumeric data as groups of bits. Binary codes are classified as weighted or non-weighted, reflective or non-reflective, and sequential or non-sequential. Common binary codes include ASCII, EBCDIC, Hollerith, BCD, excess-3, and Gray codes. Error detecting and correcting codes are also discussed which add extra bits to detect or correct errors during data transmission. Examples of different binary codes are provided.
JK flip-flops have two outputs, Q and Q', and four modes of operation: hold, set, reset, toggle. The primary output is Q. There are two stable states that can store state information. JK flip-flops are used for data storage in registers, counting in counters, and frequency division. They can divide the frequency of a periodic waveform in half by toggling on each input clock pulse.
This document provides information about different types of counters, including asynchronous counters, synchronous counters, MSI counters, and specific counter integrated circuits. It defines counters and describes their basic characteristics. It discusses asynchronous ripple counters and their timing. It provides examples of decade and binary counters. It describes synchronous counters and MSI counters like the 74LS163 4-bit synchronous counter. Finally, it provides truth tables, logic diagrams, and application information for common counter ICs like the 7490, 7492, 7493, and 74LS163.
This document discusses ripple counters and their characteristics:
- Ripple counters have a modulus (MOD) which is the number of states the counter cycles through before repeating. The MOD is equal to 2n where n is the number of flip-flops.
- State transition diagrams graphically represent the sequence of states a counter goes through with each clock pulse.
- Common integrated circuits used for ripple counters include the 74LS90, 74LS92, 74LS93 and 74HC390. The 74LS93 and 74HC390 can be configured to count to different MODs by controlling enable inputs.
- The internal logic of the 74LS93 is shown, with the clock pulse applied to
This document discusses latches and flip flops, which are types of sequential logic circuits. It describes the basic components and functioning of latches like SR latches, D latches, and gated latches. For flip flops, it covers SR flip flops, D flip flops, JK flip flops, and master-slave flip flops. The key differences between latches and flip flops are that latches do not have a clock input while flip flops are edge-triggered by a clock signal. Latches and flip flops are used as basic storage elements in more complex sequential circuits and in computer components like registers and RAM.
- Boolean algebra uses binary values (1/0) to represent true/false in digital circuits.
- The basic Boolean operations are AND, OR, and NOT. Truth tables and Boolean expressions can both be used to represent the functions of circuits.
- Boolean expressions can be simplified using algebraic rules like commutative, distributive, DeMorgan's, and absorption laws. This allows simpler circuit implementations.
This document provides an overview of digital logic circuits and sequential circuits. It discusses various logic gates like OR, AND, NOT, NAND, NOR and XOR gates. It explains their truth tables and symbols. It also covers Boolean algebra, map simplification using K-maps, combinational circuits like multiplexers, demultiplexers, encoders and decoders. Finally, it describes different types of flip-flops like SR, D, JK and T flip-flops which are used to build sequential circuits that have memory and can store past states.
DIGITAL ELECTRONICS- Logic Gates
The AND gate
The OR gate
The NOT gate (or inverter)
The NAND gate
The NOR gate
The Exclusive OR gate
The Exclusive NOR gate
This document defines and classifies different types of binary codes. It explains that binary codes represent numeric and alphanumeric data as groups of bits. Binary codes are classified as weighted or non-weighted, reflective or non-reflective, and sequential or non-sequential. Common binary codes include ASCII, EBCDIC, Hollerith, BCD, excess-3, and Gray codes. Error detecting and correcting codes are also discussed which add extra bits to detect or correct errors during data transmission. Examples of different binary codes are provided.
JK flip-flops have two outputs, Q and Q', and four modes of operation: hold, set, reset, toggle. The primary output is Q. There are two stable states that can store state information. JK flip-flops are used for data storage in registers, counting in counters, and frequency division. They can divide the frequency of a periodic waveform in half by toggling on each input clock pulse.
Booth's multiplication algorithm multiplies two signed binary numbers in two's complement notation. It was invented by Andrew Donald Booth in 1950. The algorithm inspects two bits of the multiplier at a time, and either adds, subtracts, or leaves unchanged the partial product depending on whether the bits are 10, 01, or the same. It shifts the partial product and multiplier arithmeticly to the right after each step to inspect the next bits.
This document discusses different types of binary codes used to represent digital data, including weighted codes like BCD and non-weighted codes like Gray code. It provides details on code conversions between binary, Gray code, BCD, and excess-3 code. Conversion methods are described algorithmically and using logic gates. Truth tables are given to illustrate the bit patterns for conversions between BCD and excess-3 code.
This document discusses decoders and encoders. It defines a decoder as a circuit that accepts a binary input and activates only one output corresponding to the input. An encoder is the inverse, converting an active input to a coded output. Various types of decoders and encoders are described, including 2-to-4 decoders, 3-to-8 decoders, priority encoders, decimal-to-BCD encoders, and octal-to-binary encoders. Truth tables and logic diagrams are provided as examples. Expansion of decoders using multiple lower-order decoders is also covered.
This document discusses combinational logic circuits such as adders, subtractors, multipliers, decoders, and multiplexers. It provides circuit diagrams and truth tables for half adders, full adders, half subtractors, full subtractors, decoders, and multiplexers. It also describes how to build binary adders and subtractors using these basic components and how multiplication of binary numbers is performed.
The document discusses binary multipliers. It describes how a combinational multiplier circuit performs multiplication by multiplying the multiplicand by each bit of the multiplier starting from the least significant bit. Each multiplication forms a partial product that is shifted left. The final product is the sum of the partial products. It then provides examples of 2-bit by 2-bit and 4-bit by 3-bit binary multipliers, showing how the partial products are generated using AND gates and added using half adders or full adders.
This document discusses universal logic gates. It explains that NAND and NOR gates are universal because any boolean logic function can be implemented using only these gate types. The document provides truth tables to show how to construct NOT, AND and OR gates using only NAND gates, and how to construct them using only NOR gates. Examples are given of implementing sum-of-products and product-of-sums logic functions using two-level logic with NAND and NOR gates respectively. Applications mentioned include use in manufacturing logic circuits and flash memory.
This document provides an overview of sequential circuits and flip-flops. It discusses the objectives of sequential circuits and various types of flip-flops like SR, JK, D and T flip-flops. It explains what flip-flops are, how they work, and where they are used. It also covers the conversions between different types of flip-flops like SR to JK, JK to SR, SR to D, and D to SR. Diagrams and truth tables are provided to illustrate these conversions.
This document provides an outline for a course on digital logic design. It includes the course title and credit hours, topics that will be covered such as Boolean algebra, logic gates, combinational and sequential circuits, programmable logic devices, and memory. It also lists recommended textbooks and provides the grading breakdown. Examples of analogue and digital quantities, signals, and number systems are given. Common logic gates such as AND, OR, NOT, NAND and NOR are described along with their truth tables and applications. Combinational circuits, functional devices, sequential circuits and memory are also introduced.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
Shift registers are constructed using flip-flops connected in a way to store and transfer digital data. Data is stored at the Q output of D flip-flops during a clock pulse. Shift registers allow data to be transferred between flip-flops upon a clock edge. There are four types of data movement: serial in serial out, serial in parallel out, parallel in serial out, and parallel in parallel out. Shift registers can be loaded serially or in parallel and are used in applications like pseudo random pattern generators, ring counters, and Johnson counters.
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 discusses different types of counters used in digital circuits. It defines a counter as a sequential circuit that cycles through a sequence of states in response to clock pulses. Binary counters count in binary and can count from 0 to 2n-1 with n flip-flops. Asynchronous counters have flip-flops that are not triggered simultaneously by a clock, while synchronous counters use a common clock for all flip-flops. Other counter types include ring counters, Johnson counters, and decade counters. The document provides examples of binary, asynchronous, and synchronous counters and discusses their applications in areas like timing sequences and addressing memory.
This document discusses digital adders and subtracters. It begins by explaining half adders and full adders, which are used to add binary numbers. It then discusses how to design multi-bit adders using full adders as building blocks. Different approaches for subtraction using full adders and full subtracters are also covered. The document provides circuit diagrams and truth tables to illustrate the designs of basic digital addition and subtraction components.
This document describes a circuit to convert between binary coded decimal (BCD) and excess-3 code. It begins by explaining that code converters are needed when different systems use different codes to represent the same information. It then provides background on BCD, which represents each decimal digit with 4 bits, and excess-3 code, which adds 0011 to each BCD value. The document presents the truth table for the conversion and uses Karnaugh maps to derive the Boolean expressions for converting each output bit. It concludes by mentioning some early applications of excess-3 code in computers, cash registers and calculators.
This document discusses digital logic circuits and binary logic. It begins with an overview of binary logic, logic gates like NAND, NOR and XOR, and Boolean algebra. It then covers analog vs digital signals, quantization, and converting between analog and digital formats. Various representations of digital designs are presented, including truth tables, Boolean algebra, and schematics. Common logic gates and their representations are described. The document discusses design methodologies and analyses, as well as simulation of logic circuits. It also covers elementary binary logic functions, basic identities of Boolean algebra, and converting between Boolean expressions and logic circuits.
Chapter 4. logic function and boolean algebraAshish KC
- Boolean algebra is used to analyze and design digital logic circuits and determines logical propositions as either true or false. It uses basic logic gates like AND, OR, and NOT.
- AND gates output 1 only if all inputs are 1, while OR gates output 1 if any input is 1. NOT gates invert the input. More complex gates can be made by combining basic gates, like NAND (AND with output inverted) and NOR (OR with output inverted).
- Boolean algebra has laws like commutative, distributive, complement, identity, and associative laws that define the operations of logical variables and simplify expressions. Together, Boolean algebra and logic gates form the foundation of digital circuit and computer design.
Weighted codes assign a numeric weight or value to each digit position in a number, with the sum of the digit values representing the number. BCD is a weighted code where each of the 4 bits is assigned a weight from 1 to 8. Non-weighted codes do not assign positional weights, with Gray code and excess-3 code given as examples. BCD addition follows the same rules as binary addition, while conversion between BCD and decimal is simpler than binary. Gray code is a non-weighted code where each number differs from the previous by one bit. Excess-3 code is a 4-bit non-weighted code used with BCD, where each decimal digit is converted to BCD after adding 3.
This document provides an overview of binary codes and Boolean algebra concepts. It discusses various binary codes like BCD, excess-3, and Gray codes. It also covers logical operations in Boolean algebra like AND, OR, and NOT. Properties of Boolean algebra like duality, De Morgan's laws, and absorption laws are explained. Digital logic gates are introduced as implementations of Boolean functions.
The document discusses combinational logic circuits including:
1) Combinational logic circuits take inputs and provide outputs depending on the input combinations without any internal stored memory. The document discusses finding the number of inputs/outputs, writing truth tables, minimizing functions, and implementing circuits using logic gates.
2) Common combinational logic circuits are discussed including half adders, full adders, subtractors, comparators, and code converters. Truth tables and minimized logic expressions are provided for these circuits.
3) Implementation of combinational logic circuits using logic gates like AND, OR, NAND, NOR is explained. Examples of half adder, full adder, and code converter logic diagrams are also given.
The document provides information about Unit 2 of a course which includes:
- Boolean algebra rules and laws such as commutative, associative, distributive for AND, OR and inversion. De Morgan's theorem.
- Simplifying logic equations using Boolean algebra rules and Karnaugh maps up to 4 bits.
- Converting between binary and gray codes.
- Minimizing logic expressions using Karnaugh maps.
Booth's multiplication algorithm multiplies two signed binary numbers in two's complement notation. It was invented by Andrew Donald Booth in 1950. The algorithm inspects two bits of the multiplier at a time, and either adds, subtracts, or leaves unchanged the partial product depending on whether the bits are 10, 01, or the same. It shifts the partial product and multiplier arithmeticly to the right after each step to inspect the next bits.
This document discusses different types of binary codes used to represent digital data, including weighted codes like BCD and non-weighted codes like Gray code. It provides details on code conversions between binary, Gray code, BCD, and excess-3 code. Conversion methods are described algorithmically and using logic gates. Truth tables are given to illustrate the bit patterns for conversions between BCD and excess-3 code.
This document discusses decoders and encoders. It defines a decoder as a circuit that accepts a binary input and activates only one output corresponding to the input. An encoder is the inverse, converting an active input to a coded output. Various types of decoders and encoders are described, including 2-to-4 decoders, 3-to-8 decoders, priority encoders, decimal-to-BCD encoders, and octal-to-binary encoders. Truth tables and logic diagrams are provided as examples. Expansion of decoders using multiple lower-order decoders is also covered.
This document discusses combinational logic circuits such as adders, subtractors, multipliers, decoders, and multiplexers. It provides circuit diagrams and truth tables for half adders, full adders, half subtractors, full subtractors, decoders, and multiplexers. It also describes how to build binary adders and subtractors using these basic components and how multiplication of binary numbers is performed.
The document discusses binary multipliers. It describes how a combinational multiplier circuit performs multiplication by multiplying the multiplicand by each bit of the multiplier starting from the least significant bit. Each multiplication forms a partial product that is shifted left. The final product is the sum of the partial products. It then provides examples of 2-bit by 2-bit and 4-bit by 3-bit binary multipliers, showing how the partial products are generated using AND gates and added using half adders or full adders.
This document discusses universal logic gates. It explains that NAND and NOR gates are universal because any boolean logic function can be implemented using only these gate types. The document provides truth tables to show how to construct NOT, AND and OR gates using only NAND gates, and how to construct them using only NOR gates. Examples are given of implementing sum-of-products and product-of-sums logic functions using two-level logic with NAND and NOR gates respectively. Applications mentioned include use in manufacturing logic circuits and flash memory.
This document provides an overview of sequential circuits and flip-flops. It discusses the objectives of sequential circuits and various types of flip-flops like SR, JK, D and T flip-flops. It explains what flip-flops are, how they work, and where they are used. It also covers the conversions between different types of flip-flops like SR to JK, JK to SR, SR to D, and D to SR. Diagrams and truth tables are provided to illustrate these conversions.
This document provides an outline for a course on digital logic design. It includes the course title and credit hours, topics that will be covered such as Boolean algebra, logic gates, combinational and sequential circuits, programmable logic devices, and memory. It also lists recommended textbooks and provides the grading breakdown. Examples of analogue and digital quantities, signals, and number systems are given. Common logic gates such as AND, OR, NOT, NAND and NOR are described along with their truth tables and applications. Combinational circuits, functional devices, sequential circuits and memory are also introduced.
Boolean algebra is an algebra of logic developed by George Boole between 1815-1864 to represent logical statements as an algebra of true and false. It is used to perform logical operations in digital computers by representing true as 1 and false as 0. The fundamental logical operators are AND, OR, and NOT. Boolean algebra expressions can be represented in sum of products (SOP) form or product of sums (POS) form and minimized using algebraic rules or Karnaugh maps. Minterms and maxterms are used to derive Boolean functions from truth tables in canonical SOP or POS form.
Shift registers are constructed using flip-flops connected in a way to store and transfer digital data. Data is stored at the Q output of D flip-flops during a clock pulse. Shift registers allow data to be transferred between flip-flops upon a clock edge. There are four types of data movement: serial in serial out, serial in parallel out, parallel in serial out, and parallel in parallel out. Shift registers can be loaded serially or in parallel and are used in applications like pseudo random pattern generators, ring counters, and Johnson counters.
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 discusses different types of counters used in digital circuits. It defines a counter as a sequential circuit that cycles through a sequence of states in response to clock pulses. Binary counters count in binary and can count from 0 to 2n-1 with n flip-flops. Asynchronous counters have flip-flops that are not triggered simultaneously by a clock, while synchronous counters use a common clock for all flip-flops. Other counter types include ring counters, Johnson counters, and decade counters. The document provides examples of binary, asynchronous, and synchronous counters and discusses their applications in areas like timing sequences and addressing memory.
This document discusses digital adders and subtracters. It begins by explaining half adders and full adders, which are used to add binary numbers. It then discusses how to design multi-bit adders using full adders as building blocks. Different approaches for subtraction using full adders and full subtracters are also covered. The document provides circuit diagrams and truth tables to illustrate the designs of basic digital addition and subtraction components.
This document describes a circuit to convert between binary coded decimal (BCD) and excess-3 code. It begins by explaining that code converters are needed when different systems use different codes to represent the same information. It then provides background on BCD, which represents each decimal digit with 4 bits, and excess-3 code, which adds 0011 to each BCD value. The document presents the truth table for the conversion and uses Karnaugh maps to derive the Boolean expressions for converting each output bit. It concludes by mentioning some early applications of excess-3 code in computers, cash registers and calculators.
This document discusses digital logic circuits and binary logic. It begins with an overview of binary logic, logic gates like NAND, NOR and XOR, and Boolean algebra. It then covers analog vs digital signals, quantization, and converting between analog and digital formats. Various representations of digital designs are presented, including truth tables, Boolean algebra, and schematics. Common logic gates and their representations are described. The document discusses design methodologies and analyses, as well as simulation of logic circuits. It also covers elementary binary logic functions, basic identities of Boolean algebra, and converting between Boolean expressions and logic circuits.
Chapter 4. logic function and boolean algebraAshish KC
- Boolean algebra is used to analyze and design digital logic circuits and determines logical propositions as either true or false. It uses basic logic gates like AND, OR, and NOT.
- AND gates output 1 only if all inputs are 1, while OR gates output 1 if any input is 1. NOT gates invert the input. More complex gates can be made by combining basic gates, like NAND (AND with output inverted) and NOR (OR with output inverted).
- Boolean algebra has laws like commutative, distributive, complement, identity, and associative laws that define the operations of logical variables and simplify expressions. Together, Boolean algebra and logic gates form the foundation of digital circuit and computer design.
Weighted codes assign a numeric weight or value to each digit position in a number, with the sum of the digit values representing the number. BCD is a weighted code where each of the 4 bits is assigned a weight from 1 to 8. Non-weighted codes do not assign positional weights, with Gray code and excess-3 code given as examples. BCD addition follows the same rules as binary addition, while conversion between BCD and decimal is simpler than binary. Gray code is a non-weighted code where each number differs from the previous by one bit. Excess-3 code is a 4-bit non-weighted code used with BCD, where each decimal digit is converted to BCD after adding 3.
This document provides an overview of binary codes and Boolean algebra concepts. It discusses various binary codes like BCD, excess-3, and Gray codes. It also covers logical operations in Boolean algebra like AND, OR, and NOT. Properties of Boolean algebra like duality, De Morgan's laws, and absorption laws are explained. Digital logic gates are introduced as implementations of Boolean functions.
The document discusses combinational logic circuits including:
1) Combinational logic circuits take inputs and provide outputs depending on the input combinations without any internal stored memory. The document discusses finding the number of inputs/outputs, writing truth tables, minimizing functions, and implementing circuits using logic gates.
2) Common combinational logic circuits are discussed including half adders, full adders, subtractors, comparators, and code converters. Truth tables and minimized logic expressions are provided for these circuits.
3) Implementation of combinational logic circuits using logic gates like AND, OR, NAND, NOR is explained. Examples of half adder, full adder, and code converter logic diagrams are also given.
The document provides information about Unit 2 of a course which includes:
- Boolean algebra rules and laws such as commutative, associative, distributive for AND, OR and inversion. De Morgan's theorem.
- Simplifying logic equations using Boolean algebra rules and Karnaugh maps up to 4 bits.
- Converting between binary and gray codes.
- Minimizing logic expressions using Karnaugh maps.
The document discusses various types of combinational logic circuits including arithmetic circuits like half/full adders and subtractors, magnitude comparators, and code conversion circuits like encoders and decoders. It provides details on their structure, truth tables, and logic expressions. Specific circuits are explained like 4-bit parallel adders, decimal to binary coded decimal encoders, and 1-bit and 2-bit magnitude comparators built using logic gates.
The document discusses digital logic circuits including comparators and code converters. It describes:
1) How an XOR gate can be used as a 2-bit comparator and how additional gates are needed to compare numbers with more bits.
2) How a 4-bit magnitude comparator like the 74LS85 works by starting with the most significant bit and propagating the result through cascading inputs.
3) Methods for converting between binary coded decimal (BCD) and other codes like binary, gray code, and excess-3 (XS3) using logic gates and truth tables.
- There are two classes of logic circuits: combinational circuits and sequential circuits.
- A combinational circuit consists of logic gates where the output depends only on the current inputs.
- Common combinational circuits include arithmetic functions, data transmission functions, and code converters.
- Combinational circuits can be analyzed using Boolean functions and truth tables to determine the function and design circuits.
1. The document discusses digital number systems and binary codes. It explains how to convert between different number bases, such as decimal, binary, and octal. Arithmetic operations like addition, subtraction, multiplication and division are demonstrated for binary numbers.
2. Various binary coding techniques are described to represent decimal digits using a sequence of binary digits. Weighted and non-weighted codes like BCD, excess-3, and Gray codes are explained.
3. Error-detecting and correcting codes like single parity check codes and Hamming codes are covered. The construction and working of Hamming codes to detect and correct single bit errors are demonstrated through examples.
In this slide, the following topics are discussed. Radix number system, Binary number system, Octal, Hexadecimal, Octal to Binary, Binary to Octal, Hexadecimal to binary, Binary to Hexadecimal, BCD codes, Gray codes, one's complement, two's complement, signed magnitude number system, fixed point representation, floating point representation and their conversion.
The document discusses combinational circuits and provides examples. It can be summarized as:
1) Combinational circuits are digital circuits with outputs that are functions of current inputs only, with no internal stored state or feedback. Their outputs may change instantly due to input changes.
2) Analysis and design of combinational circuits involves determining the circuit function from its truth table or logic expressions, or designing a circuit from a given function.
3) Examples include 7-segment decoders, binary adders, and BCD adders which are analyzed using truth tables and designed using basic logic gates.
This document discusses combinational circuit design and provides examples of various combinational logic circuits. It begins with an introduction that defines combinational and sequential circuits. The remainder of the document provides details on specific combinational logic circuits including half adders, full adders, subtractors, encoders, decoders, multiplexers, comparators, and code converters. Worked examples are provided for each circuit type using truth tables, Karnaugh maps, and logic diagrams. Applications of decoders for implementing functions like a full adder are also described.
The document summarizes basic digital logic gates and components including NOT, AND, OR, NAND, NOR, XOR, XNOR gates. It also discusses multiplexers, demultiplexers, half/full adders, half/full subtractors, encoders, decoders, and conversions between binary and gray codes.
The document discusses machine instructions and programs, including:
- Number representations like binary, decimal, and signed binary
- Converting between decimal and binary numbers
- Representations of signed integers like sign-magnitude, one's complement, and two's complement
- Calculating the maximum and number of decimal numbers that can be represented in a given number of bits
This document provides an overview of logic gates and Boolean algebra. It discusses logic gates like AND, OR, and NOT. It reviews Boolean algebra concepts such as Boolean variables being limited to 1 or 0. It also covers converting between Boolean expressions and logic circuits, adding binary numbers, and memory elements like flip-flops.
The document discusses binary numbers and arithmetic. It covers topics like addition, subtraction, multiplication in binary, and different methods for representing signed integers like two's complement. It explains how two's complement works by using bitwise operations to represent negative numbers. For example, it shows that adding two positive 8-bit binary numbers in two's complement is simply the bitwise addition, while subtraction can be performed by adding the number and the two's complement of the subtrahend. The document also discusses issues like carry vs overflow that can occur during binary arithmetic operations.
The document discusses Gray code, which is a binary numbering system where two successive numbers differ in only one bit. This reduces switching errors during transitions between numbers. Gray code is used in digital communications and applications where normal binary could produce errors. The document provides examples to show how decimal numbers convert to binary and Gray code. In binary, more bits may change between numbers, while Gray code ensures only one bit changes.
This document discusses combinational logic circuits using MSI (Medium Scale Integration) and LSI (Large Scale Integration) components. It covers various MSI components like adders, decoders, encoders, multiplexers that are used as basic building blocks. Specific circuits discussed include 4-bit parallel adder, BCD adder, magnitude comparator, priority encoder, octal to binary encoder, decoder and their applications in implementing Boolean functions using multiplexers.
This document discusses various combinational logic circuits including encoders, decoders, multiplexers, and parity generators. It provides details on 4-to-2 encoders and describes how they encode 4 input lines into 2 output lines. It also discusses priority encoders, octal-to-binary encoders, and multiplexers with examples of 4-to-1 and 8-to-1 multiplexer truth tables. The document concludes with explanations of exclusive OR gates, equivalence operations, and how to implement Boolean functions using multiplexers.
The document discusses combinational circuits and their analysis and design. It provides the following key points:
1) Combinational circuits have outputs that are a function of inputs only, with no feedback or memory. When inputs change, outputs may change after a delay.
2) To analyze a combinational circuit, its function is determined from either a boolean expression or truth table. To design one, a function is specified and a circuit is determined to achieve it.
3) Analysis examples include deriving boolean expressions and truth tables from circuits. Design examples include creating circuits to achieve specified functions like binary addition and BCD to excess-3 conversion.
The document discusses different number systems including binary, octal, decimal, and hexadecimal. It explains that number systems have a radix or base, which determines the set of symbols used and their positional values. The key representations for binary numbers discussed are sign-magnitude, one's complement, and two's complement, which provide different methods for representing positive and negative numbers. The document provides examples of addition, subtraction, multiplication, and division operations in binary.
Rainfall intensity duration frequency curve statistical analysis and modeling...bijceesjournal
Using data from 41 years in Patna’ India’ the study’s goal is to analyze the trends of how often it rains on a weekly, seasonal, and annual basis (1981−2020). First, utilizing the intensity-duration-frequency (IDF) curve and the relationship by statistically analyzing rainfall’ the historical rainfall data set for Patna’ India’ during a 41 year period (1981−2020), was evaluated for its quality. Changes in the hydrologic cycle as a result of increased greenhouse gas emissions are expected to induce variations in the intensity, length, and frequency of precipitation events. One strategy to lessen vulnerability is to quantify probable changes and adapt to them. Techniques such as log-normal, normal, and Gumbel are used (EV-I). Distributions were created with durations of 1, 2, 3, 6, and 24 h and return times of 2, 5, 10, 25, and 100 years. There were also mathematical correlations discovered between rainfall and recurrence interval.
Findings: Based on findings, the Gumbel approach produced the highest intensity values, whereas the other approaches produced values that were close to each other. The data indicates that 461.9 mm of rain fell during the monsoon season’s 301st week. However, it was found that the 29th week had the greatest average rainfall, 92.6 mm. With 952.6 mm on average, the monsoon season saw the highest rainfall. Calculations revealed that the yearly rainfall averaged 1171.1 mm. Using Weibull’s method, the study was subsequently expanded to examine rainfall distribution at different recurrence intervals of 2, 5, 10, and 25 years. Rainfall and recurrence interval mathematical correlations were also developed. Further regression analysis revealed that short wave irrigation, wind direction, wind speed, pressure, relative humidity, and temperature all had a substantial influence on rainfall.
Originality and value: The results of the rainfall IDF curves can provide useful information to policymakers in making appropriate decisions in managing and minimizing floods in the study area.
An improved modulation technique suitable for a three level flying capacitor ...IJECEIAES
This research paper introduces an innovative modulation technique for controlling a 3-level flying capacitor multilevel inverter (FCMLI), aiming to streamline the modulation process in contrast to conventional methods. The proposed
simplified modulation technique paves the way for more straightforward and
efficient control of multilevel inverters, enabling their widespread adoption and
integration into modern power electronic systems. Through the amalgamation of
sinusoidal pulse width modulation (SPWM) with a high-frequency square wave
pulse, this controlling technique attains energy equilibrium across the coupling
capacitor. The modulation scheme incorporates a simplified switching pattern
and a decreased count of voltage references, thereby simplifying the control
algorithm.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Design and optimization of ion propulsion dronebjmsejournal
Electric propulsion technology is widely used in many kinds of vehicles in recent years, and aircrafts are no exception. Technically, UAVs are electrically propelled but tend to produce a significant amount of noise and vibrations. Ion propulsion technology for drones is a potential solution to this problem. Ion propulsion technology is proven to be feasible in the earth’s atmosphere. The study presented in this article shows the design of EHD thrusters and power supply for ion propulsion drones along with performance optimization of high-voltage power supply for endurance in earth’s atmosphere.
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
2. The electronics signals are continuous and
can have any value over a given range,
are called analog signal.
The electrical signal which have only two
discreet value or level (high and low), is
called digital signal. Actual values of the
signal are unimportant.
3. In this system, if 0 and 1 refer to the low and high
values respectively, the system is termed a
positive logic system.
On the contrary, if 1 and 0 refer to the low and high
values respectively, the system is termed a
negative logic system.
The signal between 0 and 1 volt can be recognized
as binary 0, between 3 and 5 volt can be taken as
binary 1. In digital system functions only in two
state, i.e. in a binary manner. The voltage is only
leveled low or high; its exact value is immaterial.
4. A binary code represents text, computer
processor instructions, or any
other data using a two-symbol system. The
two-symbol system used is often the binary
number system's 0 and 1.
The binary code assigns a pattern of binary
digits, also known as bits, to each character,
instruction, etc. For example, a
binary string of eight bits can represent any of
256 possible values and can therefore
represent a wide variety of different items.
8. The Binary-coded Decimal uses the binary
number system to specify the decimal
numbers 0 to 9.
It has four bits. The weights of the first
position is 20 (1), the second 21(2), the third
22(4), and the fourth 23(8). Reading from left to
right, the weights 8-4-2-1, hence it is called
8421 code.
Valid BCD code are : 0000 to 1001
Invalid BCD code are :1010 to 1111
9. As the name indicates, the excess-3
represents a decimal number, in binary
form, as a number greater than 3. An
excess-3 code is obtained by adding 3 to a
decimal number.
Valid excess-3 code : 0011 to 1100
Invalid excess-3 code :[0000 to 0010] and
[1101 to 1111]
10. The Gray Code belongs to a class of code
called minimum-change code, in which only
one bit in the code group changes when
moving from one step to another step.
The Gray Code is a non-weighted code.
Therefore it is not suitable arithmetic
operations but finds applications in
input/output devices and in some types of
analog to digital converters.
11. A code converters is a logic circuits whose
bit patterns representing numbers (or
characters) in one code and whose
outputs are the corresponding
representations in another code.
Code converters are usually multiple
output circuits.
12. The K-map method of solving the
logical expressions is referred to
as the graphical technique of
simplifying Boolean expressions.
K-maps are also referred to as 2D
truth tables as each K-map is
nothing but a different format of
representing the values present in
a one-dimensional truth table.
In K-maps, the rows and the
columns of the table use Gray
code-labeling which in turn
represent the values of the
corresponding input variables. This
means that each K-map cell can
be addressed using a unique Gray
Code-Word
13.
14. Minterm expansion
will
be ∑m(4,5,7,8,10,11,
13,14) + ∑d (0,1,2)
Maxterm expansion
will be
∏M(3,6,9,12,15) · ∏D
(0,1,2)
15. we have to fill the K-
map cells with one for
each minterm, zero
for each maxterm,
and X for Don't Care
terms.
The procedure is to
be repeated for every
single output variable.
16. The process has to be initiated by grouping
the bits which lie in adjacent cells such that
the group formed contains the maximum
number of selected bits. This means that for
an n-variable K-map with 2ncells,
The procedure must be applied for all
adjacent cells of the K-map, even when they
appear to be not adjacent—the top row is
considered to be adjacent to the bottom row
and the rightmost column is considered to be
adjacent to the leftmost column
A bit appearing in one group can be repeated
in another group provided that this leads to
the increase in the resulting group-size.
Don’t Care conditions are to be considered
for the grouping activity if and only if they
help in obtaining a larger group.
Otherwise, they are to be neglected.
17. For each of the resulting groups,
we have to obtain the
corresponding logical expression
in terms of the input-variables. This
can be done by expressing the bits
which are common amongst the
Gray code-words which represent
the cells contained within the
considered group.
Thus, Y =
B̅ D̅ + A̅ C̅ + A̅ BD + BC̅ D + AB̅ C
+ ACD̅
OR Y = (A+B) (B+C+D̅ ) (A+C̅ +D)
(A̅ +B̅ +C+D) (A̅ +B̅ +C̅ +D̅ )
32. 4-BIT BINARY 4-BIT BCD
B4 B3 B2 B1 Y4 Y3 Y2 Y1
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
X X X X
X X X X
X X X X
X X X X
X X X X
X X X X
33. FOR Y4=B4 FOR Y3=B3
B2B1
B4B3
00 01 11 10
00 0 0 0 0
01 0 0 0 0
11 X X X X
10 1 1 X X
B2B1
B4B3
00 01 11 10
00 0 0 1 1
01 1 1 1 1
11 X X X X
10 0 0 X X
34. FOR Y2=B2 FOR Y1=B1
B2B1
B4B3
00 01 11 10
00 0 0 1 1
01 0 0 1 1
11 X X X X
10 0 0 X X
B2B1
B4B3
00 01 11 10
00 0 1 1 0
01 0 1 1 0
11 X X X X
10 0 1 X X
39. FOR Y2= B2.B1+B2.B1
FOR Y1=B2.B1+B2.B1
=B1
B2B1
B4B3
00 01 11 10
00 1 0 1 0
01 1 0 1 0
11 X X X X
10 1 0 X X
B2B1
B4B3
00 01 11 10
00 1 0 0 1
01 0 0 0 1
11 X X X X
10 1 0 X X
44. FOR B2=Y2 ⊕Y1
FOR B1=Y2.Y1+Y2.Y1
=Y1
Y2Y1
Y4Y3
00 01 11 10
00 X X 0 X
01 0 1 0 1
11 X X X X
10 0 1 0 1
Y2Y1
Y4Y3
00 01 11 10
00 X X 0 X
01 1 0 0 1
11 1 X X X
10 1 0 X 1
49. ASCII CODE
EBCDIC CODE
The ASCII code- American Standards Code For Information
Interchange is used in most microcomputers by its
manufacturers.
This code is represented by 7 bit binary combination
EBDIC or Extended Binary Coded Decimal Interchange Code is
used in IB equipment.
It differs from ASCII code only in its grouping for the different
alphanumeric characters.
It uses 8 bits for each characters.