Multiplexer Expansion Part-2

Duration: 6 min

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Inside: a video lesson and guided study material.

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.

The video features an educational lecture by Sanchit Jain on digital logic design, focusing on constructing larger multiplexers (MUX) from smaller ones. The instructor demonstrates how to build larger MUX configurations using smaller, standard MUX units. The lesson begins with a visual demonstration of constructing a 16:1 MUX using 4:1 MUXes. It then transitions to numerical problems, calculating the exact number of 4:1 MUXes required to build a 128:1 MUX, and subsequently calculating the number of 8:1 MUXes needed for a 4096:1 MUX. The lecture concludes with a theoretical summary table that generalizes the method for any m-to-n MUX construction, providing formulas for the number of levels and the total count of MUXes required.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the first problem written on the whiteboard: "Q 16 : 1 MUX using 4 : 1 MUX ?". He begins by drawing a large rectangle to represent the target 16:1 MUX. Inside, he sketches smaller rectangles to represent the 4:1 MUX components. He draws input lines on the left and connects them to the blocks. He writes the calculation "16/4 + 4/4" on the board, indicating the first step in determining the number of components needed. He circles the "4:1 MUX" text in the question to emphasize the building block.

  2. 2:00 – 5:00 02:00-05:00

    The topic shifts to a new numerical problem: "Q how many 4X1 Mux are required in order to construct 128X1?". The instructor performs a step-by-step division on the whiteboard. He writes "128/4" resulting in 32, then "32/4" resulting in 8, then "8/4" resulting in 2, and finally "2/4" resulting in 1. He sums these values to get a total of 43, writing "32 + 8 + 2 + 1 = 43 (4x1)". He then refines this calculation, writing "32 + 8 + 2 = 42 (4x1)" and "1 (2x1)" below it, suggesting a discussion on the final stage requiring a smaller MUX.

  3. 5:00 – 6:01 05:00-06:01

    The final problem asks: "Q how many 8X1 Mux are required in order to construct 4096X1?". The instructor repeats the division method: 4096/8 = 512, 512/8 = 64, 64/8 = 8, and 8/8 = 1. He writes the summation "512 + 64 + 8 + 1" and uses tally marks to visualize the counts. Finally, he displays a summary table on the screen. The table lists "Given: m X 1", "Target: n X 1", "No of levels(K) = log_m n", and "No of Mux at i^th level (x_i) = (n/m^i)". He points to the formula for "Total Mux required". A meme of a cat labeled "BORED" is visible on the right side.

The lecture follows a logical progression from concrete visualization to abstract calculation and finally to general theory. By starting with a 16:1 MUX, the instructor establishes the visual concept of cascading smaller units. He then reinforces this with the 128:1 example, forcing the student to perform the arithmetic of summing the geometric series of MUX counts. The 4096:1 example scales this up to show the method's applicability to larger systems. The concluding table serves as a cheat sheet, providing the mathematical formulas (log_m n and summation) that underpin the manual calculations performed earlier, ensuring students can solve any similar problem efficiently.

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