Cyclic Redundancy Check Using Polynomials Part-1

Duration: 6 min

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  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) using polynomial arithmetic, beginning with foundational definitions of polynomials and their degrees. The instructor establishes that binary data patterns can be mathematically represented as polynomials where the power of x corresponds to bit position and coefficients represent bit values (0 or 1). The session progresses through polynomial representation, simplification techniques that remove zero-coefficient terms, and fundamental arithmetic operations including addition and subtraction where identical terms cancel out. The pedagogical approach uses visual diagrams mapping binary sequences to polynomial expressions, demonstrating practical conversion methods essential for understanding CRC algorithms.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with definitions of polynomial degree and structure. On-screen text displays "Degree of a Polynomial" alongside the example $x^6 + x + 1$ where degree equals 6. The instructor circles the expression $4x^3 + 7x^2 + x + 1$ to highlight coefficient terminology. Visual diagrams illustrate the mapping between binary patterns like `1000011` and polynomial coefficients, establishing that powers indicate bit positions while coefficients show bit values. This foundational segment introduces the core concept that binary data can be treated as algebraic expressions.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates polynomial simplification and arithmetic operations. A slide titled "Polynomials" shows diagram 'a' converting binary `1 0 0 0 0 1 1` to $1x^6 + 0x^5 + $, which simplifies to short form $x^6 + x + 1$ by removing zero terms. The lecture then transitions to "Adding and Subtracting Polynomials," where the instructor crosses out matching terms in $(x^5 + x^4 + x^2)$ and $(x^6 + x^4 + x^2)$ to show cancellation, yielding $x^6 + x^5$. Handwritten notes below include the expression $(x^5 + x^4 + x^2) imes x^2$, demonstrating polynomial multiplication concepts.

  3. 5:00 – 5:32 05:00-05:32

    The final segment continues the polynomial arithmetic demonstration. The screen displays "Adding and Subtracting Polynomials" with the equation $(x^5 + x^4 + x^2) + (x^6 + x^4 + x^2)$ resulting in $x^6 + x^5$. To the right, a column of binary digits is written out for comparison. The instructor reinforces that identical terms are deleted during addition, a critical property for CRC calculations where XOR operations correspond to polynomial subtraction. The session concludes with these fundamental arithmetic rules established.

The lecture systematically builds understanding of polynomial representation for binary data. Key concepts include: (1) Polynomial degree equals highest power, (2) Binary-to-polynomial mapping uses powers for positions and coefficients for values, (3) Zero-coefficient terms are omitted in short form notation, (4) Addition/subtraction cancels identical terms. These principles form the mathematical foundation for CRC algorithms, where binary data manipulation becomes polynomial arithmetic over GF(2). The visual progression from definitions to simplification to operations provides a complete conceptual framework for students preparing for CRC implementation.

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