The attached narrated power point presentation explains the circuit diagrams, working principles and truth tables of Binary to Grey Code , Grey code to Binary and BCD to Excess 3 code converters using Digital ICs. The material will be useful for KTU second year Computer Science and Engineering students who prepare for the subject CSL 202, Digital Laboratory.
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 code conversion between different digital systems. It provides an example of converting between binary coded decimal (BCD) code and excess-3 code using a combinational logic circuit. The circuit is designed using a truth table to map the input and output bits. Logic gates are then used to implement the mapping and produce the output bit combinations specified by the target code. Another example provided is the design of a circuit to convert a 4-bit binary number to a 4-bit Gray code.
This document discusses various binary codes used to represent decimal numbers in digital systems, including:
- Binary coded decimal (BCD) code, which represents each decimal digit with a unique 4-bit code. BCD addition and arithmetic are explained.
- Gray code, a cyclic code where only one bit changes between adjacent numbers. Gray code is used in applications like shaft encoders due to this property. Conversion between binary and Gray code is covered.
- Other decimal codes like excess-3 code and weighted codes are mentioned for representing decimal numbers in binary. Arithmetic operations in BCD using 10's complement for signed numbers is also summarized.
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.
numbering system binary and decimal hex octalnoor300491
Hexadecimal is a base-16 number system used to compactly represent binary numbers. It uses 16 symbols - 0-9 and A-F. Counting proceeds from F to 10, then 20, etc. Binary numbers can be converted to and from hexadecimal by grouping bits into 4-bit blocks and replacing with the hex symbol. Decimal can also be converted to and from hexadecimal using multiplication/division by 16 or remainders. Hexadecimal addition follows decimal addition rules, carrying when sums exceed 15. Octal is base-8 and uses 0-7 symbols, with binary conversion replacing octal digits with 3-bit groups. Binary Coded Decimal represents each decimal digit with 4 bits for easy decimal interfacing. Gray code changes
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.
This document provides information about binary coded decimal (BCD). It begins by defining BCD as a binary encoding where each decimal digit is represented by a fixed number of bits. BCD was commonly used for displaying alphanumeric characters but is now mainly used in real-time clocks to store time in a BCD format. Each section then explains how BCD represents decimal numbers using 4 bits per digit according to positional weights, and provides examples of converting decimal numbers to BCD and vice versa. The document also covers related topics like ASCII and EBCDIC codes.
The attached narrated power point presentation explains the circuit diagrams, working principles and truth tables of Binary to Grey Code , Grey code to Binary and BCD to Excess 3 code converters using Digital ICs. The material will be useful for KTU second year Computer Science and Engineering students who prepare for the subject CSL 202, Digital Laboratory.
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 code conversion between different digital systems. It provides an example of converting between binary coded decimal (BCD) code and excess-3 code using a combinational logic circuit. The circuit is designed using a truth table to map the input and output bits. Logic gates are then used to implement the mapping and produce the output bit combinations specified by the target code. Another example provided is the design of a circuit to convert a 4-bit binary number to a 4-bit Gray code.
This document discusses various binary codes used to represent decimal numbers in digital systems, including:
- Binary coded decimal (BCD) code, which represents each decimal digit with a unique 4-bit code. BCD addition and arithmetic are explained.
- Gray code, a cyclic code where only one bit changes between adjacent numbers. Gray code is used in applications like shaft encoders due to this property. Conversion between binary and Gray code is covered.
- Other decimal codes like excess-3 code and weighted codes are mentioned for representing decimal numbers in binary. Arithmetic operations in BCD using 10's complement for signed numbers is also summarized.
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.
numbering system binary and decimal hex octalnoor300491
Hexadecimal is a base-16 number system used to compactly represent binary numbers. It uses 16 symbols - 0-9 and A-F. Counting proceeds from F to 10, then 20, etc. Binary numbers can be converted to and from hexadecimal by grouping bits into 4-bit blocks and replacing with the hex symbol. Decimal can also be converted to and from hexadecimal using multiplication/division by 16 or remainders. Hexadecimal addition follows decimal addition rules, carrying when sums exceed 15. Octal is base-8 and uses 0-7 symbols, with binary conversion replacing octal digits with 3-bit groups. Binary Coded Decimal represents each decimal digit with 4 bits for easy decimal interfacing. Gray code changes
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.
This document provides information about binary coded decimal (BCD). It begins by defining BCD as a binary encoding where each decimal digit is represented by a fixed number of bits. BCD was commonly used for displaying alphanumeric characters but is now mainly used in real-time clocks to store time in a BCD format. Each section then explains how BCD represents decimal numbers using 4 bits per digit according to positional weights, and provides examples of converting decimal numbers to BCD and vice versa. The document also covers related topics like ASCII and EBCDIC codes.
1. The document discusses various types of code conversions including binary to BCD, BCD to excess-3, and gray to excess-3. Circuit designs and truth tables are provided for each conversion.
2. Applications of different codes are covered. BCD is used for 7-segment displays. Gray code is used in shaft encoders. Excess-3 is used for subtraction.
3. The document concludes by designing a BCD to 7-segment display decoder circuit and explaining the application of gray code in shaft encoders.
This document provides an overview of a switching theory unit syllabus that includes characteristics of digital systems, types of digital circuits, number systems, Boolean algebra, error detection and correction codes like Hamming codes. It discusses combinational and sequential digital logic circuits, direct conversion between negative numbers and binary coded decimal, minimization of Boolean functions using K-map method, and properties of cyclic codes.
This document contains lecture slides on digital logic design. It covers topics like number systems, binary arithmetic operations, weighted and non-weighted binary codes, binary coded decimal, excess-3 codes, representation of signed numbers, and error detecting codes. The document includes examples and explanations of converting between different number bases, performing binary operations, and using various coding schemes. It is intended as teaching material for a course on digital logic design.
This microproject aims to convert a hexadecimal number to its equivalent binary coded decimal (BCD) representation. The algorithm divides the hexadecimal number by 64 and stores the quotient and remainder, rotates the quotient using a right rotate instruction, and adds it to the remainder to produce the BCD result. The assembly language program implements this by declaring variables, initializing the hexadecimal number, dividing and rotating values stored in registers, and outputting the final BCD number. The program achieves the goal of understanding number systems and performing conversions between hexadecimal and BCD.
This presentation is meant to discuss the basics of video compression like DCT, Color space conversion, Motion Compensation etc. It also discusses the standards like H.264, MPEG2, MPEG4 etc.
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 different binary coded decimal (BCD) codes and how to convert between binary and BCD representations. It provides examples of converting decimal numbers to their BCD equivalents using 8421 BCD code. Other BCD codes discussed include 4221 and 5421 codes. Conversion between binary and excess-3 code is also explained with an example. The document concludes with an overview of Gray code, including how to convert between binary and Gray representations using an additive process.
This document discusses different coding systems used to represent numeric and alphanumeric characters in computers. It provides details on Binary Coded Decimal (BCD), American Standard Code for Information Interchange (ASCII), Extended Binary Coded Decimal Interchange Code (EBCDIC), Gray code, and Excess-3 code. It also gives examples and step-by-step processes for converting between binary, BCD, Excess-3, and decimal number systems.
This document describes an experiment on code conversion in Verilog. It includes the conversion of binary to gray code, gray to binary code, and binary coded decimal (BCD) to excess-3 code. Verilog code modules are provided for each conversion along with output waveforms. The experiment verified the results and modeled the conversions at both the gate level and behavioral level. The learning outcome was understanding code conversion and how to derive logic expressions from Karnaugh maps.
Binary codes can be weighted or unweighted. Weighted codes assign decimal weights to bits, like the 8-4-2-1 code. BCD is a weighted code representing each decimal digit with 4 bits. Gray code has only one bit changing between adjacent codes, making it useful for encoding shaft rotations. 1's complement inverts all bits, 2's complement adds 1 to the 1's complement. These complements allow subtraction to be performed using addition by adding the complement.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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1. The document discusses various types of code conversions including binary to BCD, BCD to excess-3, and gray to excess-3. Circuit designs and truth tables are provided for each conversion.
2. Applications of different codes are covered. BCD is used for 7-segment displays. Gray code is used in shaft encoders. Excess-3 is used for subtraction.
3. The document concludes by designing a BCD to 7-segment display decoder circuit and explaining the application of gray code in shaft encoders.
This document provides an overview of a switching theory unit syllabus that includes characteristics of digital systems, types of digital circuits, number systems, Boolean algebra, error detection and correction codes like Hamming codes. It discusses combinational and sequential digital logic circuits, direct conversion between negative numbers and binary coded decimal, minimization of Boolean functions using K-map method, and properties of cyclic codes.
This document contains lecture slides on digital logic design. It covers topics like number systems, binary arithmetic operations, weighted and non-weighted binary codes, binary coded decimal, excess-3 codes, representation of signed numbers, and error detecting codes. The document includes examples and explanations of converting between different number bases, performing binary operations, and using various coding schemes. It is intended as teaching material for a course on digital logic design.
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3. Binary to Gray:
● Invented by Frank Gray.
● Unweighted code.
● Also known as Reflected Binary
Code(RBC).
● Two successive value differs
only by one bit. It reduces
switching operation.
● Use in a K-map.
4. Binary conversion to Gray conversion
Step 1: Record the MSB as it is.
Step 2: Add the MSB to the next
bit, record the sum and neglect
the carry.
Step 3: Repeat the process.
5. Gray code to Binary code conversion
Step 1:Record the MSB as it is.
Step 2:Add to the next bit if Gray code,record
the sum and neglect the carry.
Step 3:Repeat the process.
7. Binary coded decimal(BCD)
● In this code each decimal
digit is represented by a 4-bit
binary number.
● Positional weights are
8-4-2-1.
● BCD is less efficient than
Binary.
8. Conversion of Decimal to
BCD
Example:
1. 17 ==>00010111
2. 156 ==>000101010110
3. 30 ==>00110000
Conversion of BCD to Decimal
Example:
1.00011001==>19
2.01000101==>45
3.01010100==>54
25
35
22