Practice Question

Duration: 4 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-SENIOR-COMPUTER-INSTRUCTOR/paper-2-digital-logic-systems/boolean-expression/functional-completeness/asset-practice-question-2541 after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: 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
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: 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, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: Child Development, Concept of Pedagogy, Psychology, Theories, Inclusive Education, Experiential Pedagogy, Curriculum Framework & Reforms, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
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.

Loading lesson…