Cyclic Redundancy Check Using Polynomials Part-1

Duration: 6 min

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  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
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  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
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  13. Full Length Mock Tests:
  14. Sectional 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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