Hamming Codes with error detection and Correction Part-1

Duration: 12 min

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Module outline

  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
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  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
  10. 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
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces Hamming codes as single-bit error-correcting block codes with minimum distance dmin = 3, enabling detection of up to two errors or correction of one error. The instructor defines the relationship between total codeword length n, data bits k, and redundancy r using n = 2^r - 1 and k = n - r or k = 2^r - r - 1. A table maps bit positions 1 through 20 to parity bits at powers of two (p1, p2, p4, p8, p16) and data bits elsewhere, with X marks showing which positions each parity bit covers. The lecture then works the standard example r = 3, giving n = 7 and k = 4, i.e., the Hamming code C(7,4) with dmin = 3. Parity bits are placed at positions 1, 2, and 4; data bits occupy positions 3, 5, 6, and 7. Using even parity, the instructor specifies coverage sets: P1 checks positions 1, 3, 5, 7; P2 checks 2, 3, 6, 7; and P4 checks 4, 5, 6, 7. Handwritten binary sequences illustrate how each parity bit is computed from the covered positions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with the slide titled “Hamming Codes,” stating that these codes are designed with dmin = 3, meaning they can detect up to two errors or correct one single error. The instructor emphasizes that the discussion focuses on the single-bit error-correcting code, a phrase underlined on screen. The formulas n = 2^r - 1 and k = n - r or k = 2^r - r - 1 are displayed, establishing the relationship among total bits n, data bits k, and redundancy r. A table begins mapping bit positions 1 through 20 to encoded data bits, with parity bits p1, p2, p4, p8, and p16 highlighted in green under “Parity bit coverage.”

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues explaining the Hamming code structure, pointing to the slide with a pen and then gesturing while speaking. The same “Hamming Codes” slide remains visible, with the dmin = 3 bullet and the underlined focus on single-bit error correction. A hand-drawn diagram appears above the table showing two arrow segments labeled K and r, alongside a boxed formula reading k = 2^r - r - 1. The grid table maps bit positions 1 through 20 to alternating p and d labels, with X marks filling cells to show coverage by each parity bit. The instructor raises a pen to write on the board, beginning worked calculations.

  3. 5:00 – 10:00 05:00-10:00

    The lecture transitions to a concrete example. A new slide states, “For example, if r = 3, then n = 7 and k = 4. This is a Hamming code C(7, 4) with dmin = 3.” Handwritten annotations include k = 4 and a worked line y = 8 − 3 − 1, illustrating the formula application. The instructor explains that parity bits are placed at positions that are powers of two: 2^0 = 1, 2^1 = 2, and 2^2 = 4. A table maps positions 1 through 7 to P1, P2, D1, P4, D2, D3, and D4. Even-parity checks are listed: “For parity bit P1 we check position 1, 3, 5, 7,” “For parity bit P2 we check position 2, 3, 6, 7,” and “For parity bit P4 we check position 4, 5, 6, 7.” The instructor writes binary sequences on the right side of the screen and draws arrows from table positions to these sequences, demonstrating how each parity bit is calculated.

  4. 10:00 – 11:58 10:00-11:58

    The final segment reinforces the C(7,4) construction. The instructor displays the Hamming code parameters with n = 7 and k = 4, dmin = 3. The positions for parity bits are reiterated as powers of 2: 1, 2, and 4. The coverage sets for each parity bit are restated: P1 checks positions 1, 3, 5, and 7; P2 checks 2, 3, 6, and 7; P4 checks 4, 5, 6, and 7. A 7-bit table is drawn with data bits D1 through D4 and parity bits P1, P2, and P4. The instructor annotates the board with binary values and parity calculations, using a pointer to highlight specific positions in the table. The even-parity calculation process is illustrated with handwritten binary values, showing how the parity bits are determined from the covered data positions.

The lecture progresses systematically from general principles to a specific worked example. It begins by defining Hamming codes as error-correcting codes with dmin = 3, which provides the capability to detect two errors or correct one. The mathematical foundation is established through the formulas n = 2^r - 1 and k = 2^r - r - 1, linking the number of redundancy bits r to the total codeword length n and data bits k. A visual table maps bit positions to parity and data bits, with X marks illustrating the coverage pattern: each parity bit at position 2^i checks a specific subset of positions. The lecture then applies these principles to the canonical C(7,4) code with r = 3. Parity bits are placed at positions 1, 2, and 4 (powers of two), while data bits occupy the remaining positions. The instructor explicitly lists the coverage sets for each parity bit and demonstrates even-parity calculation using handwritten binary sequences. This structured approach—definition, formula, visual mapping, and worked example—provides a clear framework for understanding Hamming code construction.

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