power point presentation regarding the number system conversions, representation of negative numbers and various codes of representations and error detection and correction codes.
Weighted codes assign a positional weight or value to each digit, where the sum of the digit values multiplied by their weights represents the number. Non-weighted codes do not assign positional weights. BCD is a weighted 4-bit code that represents the decimal digits 0-9. It uses weights of 24, 23, 22, 21 from most to least significant bit. The Gray code is a non-weighted code where each number differs from the previous by one bit. Excess-3 code is a non-weighted 4-bit BCD code where 3 is added to each decimal digit before conversion to BCD.
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.
1) Binary codes represent numbers, letters, and other data using groups of bits or symbols. Weighted binary codes follow a positional weighting principle where each bit position represents a specific weight.
2) Non-weighted codes like excess-3 code and Gray code do not assign positional weights. Gray code is used in shaft position encoders to prevent multiple bit changes that can cause problems.
3) BCD (binary coded decimal) represents each decimal digit with a 4-bit binary number, allowing representation of numbers from 0-9. BCD addition can result in numbers outside the valid 0-9 range, requiring carries between digits.
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.
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 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.
This document discusses several digital coding systems including BCD, excess-3, EBCDIC, error detection codes, Unicode, ASCII, extended ASCII, and Gray code. It provides details on each code such as the number of bits used, the symbols represented, and how the codes are derived. For example, it explains that BCD represents each decimal digit with 4 bits and excess-3 code is obtained by adding 3 to the BCD number. It also covers topics like parity bits for error detection and the properties of Gray code.
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.
Weighted codes assign a positional weight or value to each digit, where the sum of the digit values multiplied by their weights represents the number. Non-weighted codes do not assign positional weights. BCD is a weighted 4-bit code that represents the decimal digits 0-9. It uses weights of 24, 23, 22, 21 from most to least significant bit. The Gray code is a non-weighted code where each number differs from the previous by one bit. Excess-3 code is a non-weighted 4-bit BCD code where 3 is added to each decimal digit before conversion to BCD.
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.
1) Binary codes represent numbers, letters, and other data using groups of bits or symbols. Weighted binary codes follow a positional weighting principle where each bit position represents a specific weight.
2) Non-weighted codes like excess-3 code and Gray code do not assign positional weights. Gray code is used in shaft position encoders to prevent multiple bit changes that can cause problems.
3) BCD (binary coded decimal) represents each decimal digit with a 4-bit binary number, allowing representation of numbers from 0-9. BCD addition can result in numbers outside the valid 0-9 range, requiring carries between digits.
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.
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 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.
This document discusses several digital coding systems including BCD, excess-3, EBCDIC, error detection codes, Unicode, ASCII, extended ASCII, and Gray code. It provides details on each code such as the number of bits used, the symbols represented, and how the codes are derived. For example, it explains that BCD represents each decimal digit with 4 bits and excess-3 code is obtained by adding 3 to the BCD number. It also covers topics like parity bits for error detection and the properties of Gray code.
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.
This document describes a 3 credit hour course on digital electronics and logic design with the code DEL-244. It covers various topics in binary codes including weighted and non-weighted systems. Specific codes discussed include binary coded decimal, excess-3 code, gray code, and two's complement representations for negative numbers. Arithmetic operations using two's complement are also demonstrated.
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.
This document discusses decoders, which are circuits that take a binary input and activate one of multiple outputs. It provides examples of 2-to-4 and 3-to-8 decoders and their truth tables. Decoders are constructed using AND gates, with the number of gates equal to the number of outputs. Larger decoders can be built in parallel, balanced, or tree configurations, with balanced decoders requiring the fewest components.
Encoders convert decimal input to binary coded decimal (BCD) output, while decoders convert BCD input to decimal output displayed on a 7-segment display. An example encoder converts decimal numbers to their BCD coded form, while an example decoder converts BCD codes into the decimal numbers they represent, which are then shown on a 7-segment LED display. The document provides examples of encodings and decoding between decimal, BCD, and 7-segment display representations and tests the reader with questions about decoding BCD inputs.
This document provides an overview of Boolean algebra and logic gates. It introduces Boolean logic operations like AND, OR, and NOT. It covers Boolean algebra laws and De Morgan's theorems. It also discusses logic gate types like AND, OR, NOT, NAND, NOR, XOR and XNOR. Karnaugh maps are introduced as a method to simplify Boolean expressions.
The document explains about the concepts of sequential circuits in Digital electronics.
This will be helpful for the beginners in VLSI and electronics students.
Binary code represents data using 0s and 1s. Gray code is a binary system where two consecutive values differ in only one bit, making it useful for minimizing errors in digital circuits. To convert between binary and Gray code, the most significant bit will remain the same while other bits are converted using logic gates that flip values based on adjacent less significant bits.
The document discusses Karnaugh maps (K-maps), which are a tool for representing and simplifying Boolean functions with up to six variables. K-maps arrange the variables in a grid according to their binary values. Adjacent cells that differ in only one variable can be combined to simplify the function by eliminating that variable. The document provides examples of using K-maps to minimize Boolean functions in sum of products and product of sums form. It also discusses techniques like combining cells into the largest groups possible and handling don't-care conditions to further simplify expressions.
This document describes how to convert a Binary Coded Decimal (BCD) number to its equivalent binary number. It explains that BCD represents decimal numbers as 4-bit binary codes, with values 0-9 having their own codes. For values above 9, each decimal digit is represented by a 4-bit code. The document includes a truth table and Karnaugh maps to derive the logic gates needed for a BCD to binary converter circuit. It also notes that for BCD values above 9, the most significant bits in the binary output are "don't cares".
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.
This document provides information about Dr. Krishnanaik Vankdoth and his background and qualifications. It then discusses digital logic design topics like digital circuits, combinational logic, sequential circuits, logic gates, truth tables, adders, decoders, encoders, multiplexers and demultiplexers. Example circuits are provided and the functions of components like full adders, parallel adders, magnitude comparators are explained through diagrams and logic equations.
Booth's multiplication algorithm was invented by Andrew D. Booth in 1951 while studying crystallography at Birkbeck College in London. It improves the speed of computer multiplication by reducing the number of additions or subtractions needed. The algorithm uses a grid with the multiplicand in the top row, the negative multiplicand in the middle row, and the multiplier in the bottom row. It then iteratively shifts and adds or subtracts based on the last two bits of the product to build up the final result in fewer steps than standard addition methods. Several examples are provided to demonstrate how the algorithm works.
The BINARY to GRAY CODE CONVERTER is a digital circuit that is used to convert the binary input into the corresponding equivalent gray code at its output
DeMorgan's theorems state that:
1) The negation of a conjunction is the disjunction of the negations.
2) The negation of a disjunction is the conjunction of the negations.
They can be used to transform logical expressions between conjunctive and disjunctive normal form by distributing negations inward and changing conjunctions to disjunctions (or vice versa). The document provides examples of applying DeMorgan's theorems to logically equivalent expressions.
Introduction to ibm pc assembly languagewarda aziz
The Solution manual of COAL
Chapter NO 4. exercise
if anyone has Questions Regarding this exercise.
contact me on my given Email-ID.
i will guide you. Thank you!
Boolean algebra and logic circuits were introduced. Boolean algebra uses binary numbers (0,1) and logical operations like AND, OR, and NOT to simplify logic expressions. Basic logic gates like AND, OR, and NOT were explained. Logic circuits can be built using combinations of logic gates to perform complex logical functions. Boolean algebra is used to simplify logic circuits and increase the efficiency of digital devices like computers.
This document discusses digital subtractors. It defines a subtractor as an electronic logic circuit that calculates the difference between two binary numbers. There are two main types: half subtractors and full subtractors. A half subtractor is used for single bit subtraction and has two inputs, two outputs, and a truth table. A full subtractor can subtract three single bit numbers, with three inputs and two outputs defined by its truth table. Parallel binary subtractors are built by cascading multiple full subtractors to subtract larger binary numbers. Subtractors have applications in signal processing, arithmetic logic units, address calculation, and more.
This document discusses flag usage in computing. It explains that the flag register contains 16 bits that show the status of operations, with 9 bits indicating the current status. There are status flags like carry, zero, and sign that reflect the outcome of arithmetic operations. Additionally, there are control flags that direct CPU operations. Examples are provided to illustrate how specific instructions affect the flags.
1. Boolean algebra is a mathematical system used to specify and transform logic functions. It uses binary variables that take on values of 1 or 0 and logical operators like AND, OR, and NOT.
2. Logic gates implement logic functions physically using electronic components. Common gates are AND, OR, and NOT. Gates have a small but nonzero delay between input change and output change.
3. Boolean expressions can be represented using truth tables, logic diagrams, or algebraic expressions. Standard forms include sum-of-minterms and product-of-maxterms forms.
The document discusses different methods for representing negative numbers in binary, including signed bit representation and two's complement representation. Two's complement is described as a better method as it avoids having two representations for zero. The key aspects of two's complement are explained, such as how to find the two's complement of a number by flipping its bits and adding one. Examples are provided to illustrate how negative numbers are represented using two's complement. The document also discusses the range of integers that can be stored using different numbers of bytes with two's complement representation.
This document discusses 2's complement arithmetic in digital electronics. It explains that subtracting one number from another is the same as making one number negative and adding them. It then demonstrates how to represent negative numbers in binary by taking the 2's complement of a number, which involves complementing all its digits and adding 1. Various examples are provided of adding positive and negative binary numbers by taking the 2's complement of negative terms before adding. The most significant bit is identified as the sign bit that determines if a number is positive or negative.
This document describes a 3 credit hour course on digital electronics and logic design with the code DEL-244. It covers various topics in binary codes including weighted and non-weighted systems. Specific codes discussed include binary coded decimal, excess-3 code, gray code, and two's complement representations for negative numbers. Arithmetic operations using two's complement are also demonstrated.
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.
This document discusses decoders, which are circuits that take a binary input and activate one of multiple outputs. It provides examples of 2-to-4 and 3-to-8 decoders and their truth tables. Decoders are constructed using AND gates, with the number of gates equal to the number of outputs. Larger decoders can be built in parallel, balanced, or tree configurations, with balanced decoders requiring the fewest components.
Encoders convert decimal input to binary coded decimal (BCD) output, while decoders convert BCD input to decimal output displayed on a 7-segment display. An example encoder converts decimal numbers to their BCD coded form, while an example decoder converts BCD codes into the decimal numbers they represent, which are then shown on a 7-segment LED display. The document provides examples of encodings and decoding between decimal, BCD, and 7-segment display representations and tests the reader with questions about decoding BCD inputs.
This document provides an overview of Boolean algebra and logic gates. It introduces Boolean logic operations like AND, OR, and NOT. It covers Boolean algebra laws and De Morgan's theorems. It also discusses logic gate types like AND, OR, NOT, NAND, NOR, XOR and XNOR. Karnaugh maps are introduced as a method to simplify Boolean expressions.
The document explains about the concepts of sequential circuits in Digital electronics.
This will be helpful for the beginners in VLSI and electronics students.
Binary code represents data using 0s and 1s. Gray code is a binary system where two consecutive values differ in only one bit, making it useful for minimizing errors in digital circuits. To convert between binary and Gray code, the most significant bit will remain the same while other bits are converted using logic gates that flip values based on adjacent less significant bits.
The document discusses Karnaugh maps (K-maps), which are a tool for representing and simplifying Boolean functions with up to six variables. K-maps arrange the variables in a grid according to their binary values. Adjacent cells that differ in only one variable can be combined to simplify the function by eliminating that variable. The document provides examples of using K-maps to minimize Boolean functions in sum of products and product of sums form. It also discusses techniques like combining cells into the largest groups possible and handling don't-care conditions to further simplify expressions.
This document describes how to convert a Binary Coded Decimal (BCD) number to its equivalent binary number. It explains that BCD represents decimal numbers as 4-bit binary codes, with values 0-9 having their own codes. For values above 9, each decimal digit is represented by a 4-bit code. The document includes a truth table and Karnaugh maps to derive the logic gates needed for a BCD to binary converter circuit. It also notes that for BCD values above 9, the most significant bits in the binary output are "don't cares".
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.
This document provides information about Dr. Krishnanaik Vankdoth and his background and qualifications. It then discusses digital logic design topics like digital circuits, combinational logic, sequential circuits, logic gates, truth tables, adders, decoders, encoders, multiplexers and demultiplexers. Example circuits are provided and the functions of components like full adders, parallel adders, magnitude comparators are explained through diagrams and logic equations.
Booth's multiplication algorithm was invented by Andrew D. Booth in 1951 while studying crystallography at Birkbeck College in London. It improves the speed of computer multiplication by reducing the number of additions or subtractions needed. The algorithm uses a grid with the multiplicand in the top row, the negative multiplicand in the middle row, and the multiplier in the bottom row. It then iteratively shifts and adds or subtracts based on the last two bits of the product to build up the final result in fewer steps than standard addition methods. Several examples are provided to demonstrate how the algorithm works.
The BINARY to GRAY CODE CONVERTER is a digital circuit that is used to convert the binary input into the corresponding equivalent gray code at its output
DeMorgan's theorems state that:
1) The negation of a conjunction is the disjunction of the negations.
2) The negation of a disjunction is the conjunction of the negations.
They can be used to transform logical expressions between conjunctive and disjunctive normal form by distributing negations inward and changing conjunctions to disjunctions (or vice versa). The document provides examples of applying DeMorgan's theorems to logically equivalent expressions.
Introduction to ibm pc assembly languagewarda aziz
The Solution manual of COAL
Chapter NO 4. exercise
if anyone has Questions Regarding this exercise.
contact me on my given Email-ID.
i will guide you. Thank you!
Boolean algebra and logic circuits were introduced. Boolean algebra uses binary numbers (0,1) and logical operations like AND, OR, and NOT to simplify logic expressions. Basic logic gates like AND, OR, and NOT were explained. Logic circuits can be built using combinations of logic gates to perform complex logical functions. Boolean algebra is used to simplify logic circuits and increase the efficiency of digital devices like computers.
This document discusses digital subtractors. It defines a subtractor as an electronic logic circuit that calculates the difference between two binary numbers. There are two main types: half subtractors and full subtractors. A half subtractor is used for single bit subtraction and has two inputs, two outputs, and a truth table. A full subtractor can subtract three single bit numbers, with three inputs and two outputs defined by its truth table. Parallel binary subtractors are built by cascading multiple full subtractors to subtract larger binary numbers. Subtractors have applications in signal processing, arithmetic logic units, address calculation, and more.
This document discusses flag usage in computing. It explains that the flag register contains 16 bits that show the status of operations, with 9 bits indicating the current status. There are status flags like carry, zero, and sign that reflect the outcome of arithmetic operations. Additionally, there are control flags that direct CPU operations. Examples are provided to illustrate how specific instructions affect the flags.
1. Boolean algebra is a mathematical system used to specify and transform logic functions. It uses binary variables that take on values of 1 or 0 and logical operators like AND, OR, and NOT.
2. Logic gates implement logic functions physically using electronic components. Common gates are AND, OR, and NOT. Gates have a small but nonzero delay between input change and output change.
3. Boolean expressions can be represented using truth tables, logic diagrams, or algebraic expressions. Standard forms include sum-of-minterms and product-of-maxterms forms.
The document discusses different methods for representing negative numbers in binary, including signed bit representation and two's complement representation. Two's complement is described as a better method as it avoids having two representations for zero. The key aspects of two's complement are explained, such as how to find the two's complement of a number by flipping its bits and adding one. Examples are provided to illustrate how negative numbers are represented using two's complement. The document also discusses the range of integers that can be stored using different numbers of bytes with two's complement representation.
This document discusses 2's complement arithmetic in digital electronics. It explains that subtracting one number from another is the same as making one number negative and adding them. It then demonstrates how to represent negative numbers in binary by taking the 2's complement of a number, which involves complementing all its digits and adding 1. Various examples are provided of adding positive and negative binary numbers by taking the 2's complement of negative terms before adding. The most significant bit is identified as the sign bit that determines if a number is positive or negative.
This document introduces group members Md. Ilias Bappi and Md.Kawsar Hamid and presents information on number systems and conversions. It discusses the decimal number system and defines ones' complement and twos' complement in binary. It provides examples of converting between binary, decimal, octal, and hexadecimal systems using appropriate techniques like multiplying bit positions by powers of the base. Conversions include binary to decimal, octal to decimal, hexadecimal to decimal, decimal to binary, octal to binary, hexadecimal to binary, decimal to octal, octal to hexadecimal, and binary to decimal representations of fractions.
This chapter discusses digital systems and number conversion. Digital systems use discrete values rather than continuous values as in analog systems. They can provide exact outputs. The chapter covers converting between number bases, such as decimal to binary, using division or multiplication. It also addresses representing negative numbers and binary codes. The design of digital systems includes system, logic, and circuit design. Combinational and sequential circuits are introduced.
This document provides an overview of different number systems including decimal, binary, octal, and hexadecimal. It defines each system, their bases, examples of conversions between them, and their uses in computing. Decimal is base 10, binary is base 2, octal is base 8, and hexadecimal is base 16. Conversions between binary, decimal, octal and hexadecimal are demonstrated through examples. Number systems are important in computing because binary is used for electronic circuitry, octal and hexadecimal allow more compact notation than binary, and decimal is used for basic calculations.
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
This document discusses different number systems including positional and non-positional, and how to convert between decimal, binary, octal, and hexadecimal numbers. It explains that positional systems use the digit's position and value to determine its overall value, and different bases determine the maximum single digit value. Conversion between number systems involves representing values in their respective bases then performing arithmetic operations.
The document discusses computer number systems and data representation. It covers binary, octal, and hexadecimal number systems. It explains how computers use digital representation based on binary and how data is represented in memory as binary digits. It also discusses different data types, analog vs digital representation, and how various number systems are used to represent binary numbers.
This document discusses different number systems. It begins by explaining how early humans used basic counting systems before introducing concepts like zero, integers, rational and irrational numbers. It then defines different types of numbers like natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers. The rest of the document explains different base systems for representing numbers, including decimal, binary, octal and hexadecimal systems. It provides examples of converting between decimal and binary representations.
This document discusses various techniques for error detection and correction in communication networks, including:
1. Types of errors such as single-bit errors and burst errors that can occur when transmitting data.
2. The central concept of redundancy, where extra bits are added to the data and used at the receiver to detect or correct errors.
3. Popular error detection and correction codes including parity-check codes, cyclic redundancy checks (CRCs), checksums, and linear block codes. These codes add redundant bits in ways that allow the receiver to identify errors.
4. How encoders add redundant bits using techniques like modulo-2 addition and division, and how decoders analyze received codewords to detect errors based on
CDS Fundamentals of digital communication system UNIT 1 AND 2.pdfshubhangisonawane6
The document discusses various number systems including decimal, binary, hexadecimal and their conversions. It explains binary addition and subtraction using 2's complement. Binary coded decimal and gray codes are also covered. The last part discusses ASCII codes for alphanumeric representation. Key points discussed are:
- Decimal, binary and hexadecimal number systems and inter-conversions between them.
- Binary addition and subtraction using 2's complement.
- Binary coded decimal and gray codes for number representation.
- ASCII codes for alphanumeric representation in computers.
This document discusses code converters and excess-3 coding. It provides background on code converters and their use for protecting private information. It then describes excess-3 coding, which represents decimal digits using 4 bits with a value of the digit plus 3. A truth table and Karnaugh maps are used to design a circuit to convert binary coded decimal to excess-3 code. The circuit outputs are derived as logical expressions of the inputs. Applications of excess-3 coding include older computers, cash registers, and calculators.
Chapter 10: Error Correction and DetectionJeoffnaRuth
This document discusses error detection and correction techniques. It defines single-bit and burst errors and explains how redundancy is used to detect or correct errors by adding extra bits. It describes the differences between error detection and correction. Various error correction methods are presented, including forward error correction, retransmission, and the use of modular arithmetic and cyclic redundancy checks. Hardware implementations of cyclic redundancy checks are also summarized.
This document discusses different types of binary codes used to represent numeric and alphanumeric data, including:
1. Weighted codes like BCD (8421) code which use 4 binary digits to represent decimal numbers 0-9.
2. Non-weighted codes like excess-3 and Gray code.
3. Alphanumeric codes like EBCDIC and ASCII which assign binary codes to represent letters, numbers, and symbols.
4. Parity codes which are used to detect errors during data transmission by checking for an even or odd number of 1s.
The document provides examples of converting between decimal, binary, and BCD numeric representations. It also discusses alphanumeric codes like ASCII for encoding text messages
Mansoor Bashir presented on code converters and parity checkers. Code converters change coded information from one system to another, such as converting decimal to binary. Parity checkers add an extra parity bit to detect errors by making the total number of 1s either even or odd. Even parity generators add a 0 bit to make the total number of 1s even, while odd parity generators add a 1 to make the total odd. Parity checkers use logic gates to check if the received bits have the correct parity or indicate an error.
This document contains a presentation on digital logic design. It discusses topics like number systems, number base conversion, binary arithmetic operations, weighted and non-weighted binary codes, and binary coded decimal arithmetic. The presentation was created by faculty at the Institute of Aeronautical Engineering for computer science and information technology students as part of a course on digital logic design.
Unit 1 data representation and computer arithmeticAmrutaMehata
This document provides an overview of a computer organization course for first year BCA students. It covers topics like introduction to digital logic design, number systems, binary arithmetic operations, binary coded decimal, and non-weighted and weighted binary codes. The key concepts discussed include binary, octal, hexadecimal number conversions; addition, subtraction, multiplication and division in binary; 1's complement, 2's complement representations; and BCD and excess-3 coding schemes.
This document discusses error detection and correction techniques for digital data transmission. It introduces different types of errors that can occur like single-bit and burst errors. It explains that redundancy is needed to detect or correct errors. Various coding techniques are described, including block coding, linear block codes, cyclic codes, and checksums. Specific codes like parity-check codes, Hamming codes, and cyclic redundancy checks are explained in detail with examples. The document emphasizes that error detection codes can only detect certain error types, while error correction codes can correct errors.
The document discusses different number systems used in digital technologies, including decimal, binary, octal, and hexadecimal systems. It provides details on how each system works, such as having 10 symbols in decimal, 2 symbols in binary, 8 symbols in octal, and 16 symbols in hexadecimal. The document also covers error detection codes like parity and checksums that are used to detect errors in digital data transmission and storage.
This document provides information about different computer codes and number systems used in computing. It discusses binary code, which represents data as strings of 0s and 1s that computers can understand. It also describes other positional number systems like decimal, hexadecimal, octal and their use in computing. Various coding systems for converting numeric and alphanumeric data to binary formats are also covered, including binary-coded decimal and ASCII codes. Methods for converting between number systems like binary to decimal are presented.
1. The document discusses different types of codes used to represent digital data including weighted, non-weighted, alphanumeric, error detection, error correction, and binary codes.
2. It describes various binary codes like BCD, Gray, EBCDIC, and ASCII codes explaining how they represent numeric and alphanumeric data.
3. Specific codes discussed in detail include BCD, excess-3, Gray, and ASCII codes explaining their binary representations of decimal numbers and characters.
A simple parity-check code is a single-bit error-detection code where the codeword is one bit longer than the dataword. It encodes a k-bit dataword into an n-bit codeword where n=k+1. The minimum Hamming distance is 2, meaning it can detect a single bit error but cannot correct errors. It calculates the parity or XOR of the bits to generate the additional check bit and uses this to determine if an error is detected by comparing the parity of the received codeword.
The document discusses error detection and correction techniques at the data link layer. It describes how errors can occur during data transmission and the need for reliable communication. Error detection allows a receiver to detect errors while error correction enables identifying and correcting bit errors without retransmission. Common techniques discussed include parity checks, checksums, and cyclic redundancy checks which add redundant bits to detect errors. CRC is based on binary division of data and checksum on addition. Forward error correction and retransmission are compared. Coding schemes use redundancy to detect or correct errors.
Human: Thank you for the summary. Can you provide a 2 sentence summary that captures the key aspects?
This document provides an overview of error detection and correction techniques used in digital communication systems. It defines different types of errors like single bit errors and burst errors that can occur during signal transmission. It also describes various error detection methods like parity checking, checksum detection, and cyclic redundancy check (CRC). The document explains concepts of forward error correction (FEC), automatic repeat request (ARQ), and CRC checkers. It provides block diagrams of the basic ARQ system and its operations.
Lecture8_Error Detection and Correction 232.pptxMahabubAlam97
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review of number systems and codes
1. The negative number has two representations:
a. complement representation
b. sign magnitude representation
Complement representation:
There are two ways of representing complement
numbers:
a. 1’s Complement
b. 2’s Complement
2. 1’s complement of a binary number is obtained simply
by replacing each 1 by 0 and each 0 by 1. Alternately,
1’s complement of a binary can be obtained by
subtracting each bit from 1.
Example: Find 1’s complement of (i) 011001 (ii)
00100111
Solution. (i) Replace each 1 by 0 and each 0 by 1
0 1 1 0 0 1
↓ ↓ ↓ ↓ ↓ ↓
1 0 0 1 1 0
So, 1’s complement of 011001 is 100110.
3. (ii) Subtract each binary bit from 1.
1 1 1 1 1 1 1 1
–0 0 1 0 0 1 1 1
1 1 0 1 1 0 0 0 ← 1’s complement
one can see that both the method gives same
result.
2’s Complement
2’s complement of a binary number can be obtained
by adding 1 to its 1’s complement.
Example 1. Find 2’s complement of (i) 011001 (ii)
0101100
6. Before using any complement method for subtraction
equate the length of both minuendand subtrahend by
introducing leading zeros.
1’s complement subtraction following are the rules for
subtraction using 1’s complement.
1. Take 1’s complement of subtrahend.
2. Add 1’s complement of subtrahend to minuend.
3. If a carry is produced by addition then add this carry to the
LSB of result. This is called as end around carry (EAC).
4. If carry is generated from MSB in step 2 then result is
positive. If no carry generated result is negative, and is in
1’s complement form.
7. Example. Perform following subtraction using
1’s complement.
(i) 7 – 3 (ii) 3 – 7
Solution. (i) 7 – 3:
binary of 7 = (0111)2
binary of 3 = (0011)2
both numbers have equal length.
Step 1. 1’s complement of (0011)2 = (1100)2
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18. In a broad sense we can classify the codes into
five groups:
(i) Weighted Binary codes
(ii) Non-weighted codes
(iii) Error–detecting codes
(iv) Error–correcting codes
(v) Alphanumeric codes.
19. In weighted binary codes, each position of a number
represents a specific weight. The bits are multiplied by the
weights indicated; and the sum of these weighted bits gives
the equivalent decimal digit.
(a) Straight Binary coding is a method of representing a
decimal number by its binary equivalent.
20. In BCD codes, individual decimal digits are coded in
binary notation and are operated upon singly. Thus
binary codes representing 0 to 9 decimal digits are
allowed. Therefore, all BCD codes have at least
four bits (∵ min. no. of bits required to encode to
decimal digits = 4)
For example, decimal 364 in BCD
3 → 0011
6 → 0110
4 → 0100
364 → 0011 0110 0100
21. There are many binary coded decimal codes
(BCD) all of which are used to represent decimal
digits. Therefore, all BCD codes have atleast 4
bits and at least 6 unassigned or unused code
words.
Some example of BCD codes are:
(a) 8421 BCD code, sometimes referred to as the
Natural Binary Coded Decimal Code (NBCD);
(b)* Excess-3 code (XS3);
(c)** 84 –2 –1 code (+8, +4, –2, –1);
(d) 2 4 2 1 code
22.
23. Example: Lowest [643]10 into XS3 code
Decimal 6 4 3
Add 3 to each 3 3 3
Sum 9 7 6
Converting the sum into BCD code we have
9 7 6
↓ ↓ ↓
1001 0111 0110
Hence, XS3 for [643]10 = 1001 0111 0110
24. The excess 3, 8 4–2–1 and 2421 BCD codes are also known
as self complementing codes.
Self complementing property– 9’s complement of the
decimal number is easily obtained by changing 1’0 to 0’s
and 0’s to 1’s in corresponding codeword or the 9’s
complement of self complementing code word is the same
as its logical complement.
Example. The decimal digit 3 in 8.4–2–1 code is coded as
0101. The 9’s complement of 3 is 6. The decimal digit 6 is
coded as 1010 that is 1’s complement of the code for 3. This
is termed as self complementing property.
25. These codes are not positionally weighted.
This means that each position within a binary
number is not assigned a fixed value.
Excess-3 codes
Gray codes
are examples of nonweighted codes.
26. Gray code (Unit Distance code or Reflective code)
There are applications in which it is desirable to represent
numerical as well as other information with a code that
changes in only one bit position from one code word to the
nextadjacent word.
This class of code is called a unit distance code (UDC).
These are sometimes also called as ‘cyclic’, ‘reflective’ or
‘gray’ code.
These codes finds great applications in Boolean function
minimization using Karnaugh map.
27.
28. Binary information is transmitted from one device to
another by electric wires or other communication medium.
A system that can not guarantee that the data received by
one device are identical to the data transmitted by another
device is essentially useless.
Yet anytime data are transmitted from source to destination,
they can become corrupted in passage. Many factors,
including external noise, may change some of the bits from
0 to 1 or viceversa.
Reliable systems must have a mechanism for detecting and
correcting such errors.
29. In a single bit error, a 0 is changed to a 1 or a 1 is
changed to a 0.
In a burst error, multiple (two or more) bits are
changed.
The purpose of error detection code is to detect such bit
reversal errors.
Error detection uses the concept of redundancy which
means adding extra bits for detecting errors at the
destination.
30. Four types of redundancy checks are used:
Parity check or vertial redundancy check(VRC)
longitudinal redundancy check (LRC)
cyclic redundancy check (CRC) and
checksum
31. For a single bit error detection, the most common way
to achieve error detection is by means of a parity bit
A parity bit is an extra bit (redundant bit) included with
a message to make the total number of 1’s transmitted
either odd or even.
32. In LRC, a block of bits is organised in rows and columns
(table). For example, a block of 16 bits can be organised in
two rows and eight columns as shown in Fig.
We then calcualte the parity bit (even parity/odd parity, here
we are using even parity) for each column and create a new
row of 8 bits, which are the parity bits for the whole block.
33. CRC is most powerful of the redundancy checking
techniques.Cyclic redundancy check is based on
binary division.
A sequence of redundant bits called CRC or CRC
remainder is appended to the end of a data unit.
After adding CRC remainder, the resulting data
unit becomes exactly divisible by another
predetermined binary number.
At the destination this data unit is divided by the
same binary number. If there is no remainder,
then there is no error.
34. The CRC generator and CRC checker are
shown in Fig.(a) and Fig.(b) respectively.
Fig.(a) Fig.(b)
35.
36. The mechanism that we have covered upto this
point detect errors but do not correct them. Error
correction can be handled in two ways.
In one, when an error is encountered the receiver
can request the sender to retransmit entire data
unit.
In the other, a receiver can use an error correcting
code, which automatically corrects certain errors.