Cyclic Redundancy Check Part-1

Duration: 8 min

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Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  9. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware Basics
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces Cyclic Redundancy Check (CRC) as a method for error detection in data transmission, rooted in the properties of cyclic codes. The instructor begins by defining cyclic codes as a special class of linear block codes where any cyclic shift of a valid codeword results in another valid codeword. An illustrative example is provided: shifting the binary sequence 1011000 to the left yields 0110001, which remains a valid codeword. The lecture then transitions to the mechanics of CRC, explaining that a k-bit dataword is augmented by appending n-k zeros to its right-hand side. This augmented word serves as the dividend for a modulo-2 division operation using a predefined generator polynomial of size n-k+1. The remainder from this division becomes the CRC checksum, which is appended to the original dataword before transmission. The instructor demonstrates this process through detailed binary long division on a whiteboard, showing step-by-step subtraction and bit manipulation to derive the final remainder.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The session opens with a slide titled "CYCLIC CODES" defining them as linear block codes where cyclic shifts produce valid codewords. The instructor underlines the phrase "is another codeword" to emphasize this property and writes the number 10 on the display. The presentation then introduces Cyclic Redundancy Check, explaining that a k-bit dataword is augmented by appending n-k zeros. An example with k=4 and n=7 requires adding 3 zeros to create an n-bit result. Diagrams at the bottom visualize the sender's encoder and generator blocks alongside the receiver's checker components.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to a whiteboard setup for binary long division with divisor 1011 and dividend 1001000. He explains the process while gesturing towards the numbers, writing intermediate binary values such as 011 beneath the dividend to demonstrate subtraction steps. The instructor performs a binary division operation for CRC, writing down the dividend and divisor, then subtracting binary values step-by-step. The process involves bringing down subsequent bits from the dividend to continue the division until a remainder is found, with on-screen text showing "1011" and "10010000".

  3. 5:00 – 8:09 05:00-08:09

    The instructor demonstrates CRC calculation using binary division, showing two separate examples on the whiteboard. He illustrates how to append zeros to a message and divide by a generator polynomial, highlighting specific bits during division steps. The instructor crosses out zeros and carries down subsequent bits to find the remainder, with on-screen text displaying "1011", "1010", "100110", and "106116". The demonstration emphasizes XOR operations and remainder generation, highlighting the final CRC checksum.

The lecture systematically builds understanding of Cyclic Redundancy Check by first establishing the theoretical foundation of cyclic codes and then applying it to practical error detection. The core concept is that cyclic codes maintain validity under rotation, which allows for efficient implementation using polynomial division. The instructor emphasizes the augmentation process where n-k zeros are appended to a k-bit dataword, transforming it into an (n)-bit dividend. This augmented word is divided by a generator polynomial of degree n-k using modulo-2 arithmetic, which behaves like XOR operations without carries. The remainder from this division constitutes the CRC checksum. Through whiteboard demonstrations, the instructor shows how to perform binary long division step-by-step, crossing out leading zeros and bringing down bits. The visual progression from definition to calculation helps students grasp how CRC detects errors by verifying that the received message is divisible by the generator polynomial without remainder.

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