Practice Question

Duration: 4 min

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Inside: a video lesson and guided study material.

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.

The video lecture focuses on determining functional completeness in digital logic circuits, a critical concept for exams like GATE. The session begins with a problem from GATE 2015 involving two functions, f(X, Y, Z) and g(X, Y, Z), asking which set is functionally complete. The instructor then transitions to a multiple-choice question asking to identify the functionally complete set among four options involving XOR, NOT, constants, and OR. He analyzes the properties of these sets, specifically looking at linearity and preservation. He writes symbols like '~ +' and '~ .' on the whiteboard to check if the sets can generate universal gates. He selects option (b) {XOR, 1, +} as the answer. In the second half, he applies these concepts to specific functions f(a, b) = a' + b and f(a, b, c) = a' + bc'. He demonstrates how to test for preservation properties and gate generation to determine if a function is functionally complete.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video starts with a GATE 2015 question about functions f and g. The instructor then moves to a multiple-choice question: 'Which of the following is functionally complete?' with options (a) XOR, not; (b) XOR, 1, +; (c) XOR, 1, not; (d) XNOR, 1, not. He analyzes the options, writing '~ +' and '~ .' on the board to represent NOT-OR and NOT-AND. He circles option (b) and marks it, explaining that {XOR, 1, +} is functionally complete because XOR with 1 generates NOT, and {NOT, OR} is a complete set. He notes that the other options are linear or affine sets, which are not complete.

  2. 2:00 – 4:00 02:00-04:00

    The instructor analyzes f(a, b) = a' + b. He writes f(a, a) = a' + a = 1 and f(b, b) = b' + b = 1 on the board. He explains that since the function preserves 1 (outputs 1 when inputs are 1), it cannot generate the constant 0, so it is not functionally complete. Next, he analyzes f(a, b, c) = a' + bc'. He shows f(a, a, a) = a' + aa' = a', generating NOT. Then he substitutes a', b, b' to get f(a', b, b') = a'' + bb' = a + b, generating OR. Since {NOT, OR} is complete, he concludes f(a, b, c) is functionally complete. He emphasizes checking preservation of 0 and 1, monotonicity, linearity, and self-duality.

The lecture provides a comprehensive guide to testing functional completeness. It starts with a GATE problem and a multiple-choice question to introduce the concept. The instructor explains that a set is functionally complete if it can generate all Boolean functions, typically by generating NAND or NOR, or by generating a known complete set like {NOT, OR}. He demonstrates this by analyzing operator sets like {XOR, 1, +} and specific functions like f(a, b) = a' + b. Key techniques include checking for preservation of 0 and 1, linearity, and monotonicity. If a set preserves 0 or 1, it cannot be complete. If it is linear, it cannot be complete. The instructor uses board work to show substitution steps, proving that f(a, b, c) can generate NOT and OR, thus confirming its completeness.

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