Cyclic Redundancy Check Part-1

Duration: 8 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
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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