Functionally Complete Function

Duration: 7 min

This video lesson is available to enrolled students.

Return to /learn/TPSC-ASSISTANT-TECHNICAL-OFFICER/digital-logic/boolean-expression/functional-completeness/asset-functionally-complete-function after enrolling

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 lecture provides a comprehensive overview of functionally complete functions within the domain of Boolean algebra and digital logic design. It begins by establishing the foundation that all Boolean operators are derived from three fundamental ones: NOT, AND, and OR. The instructor then introduces the concept of "universal gates," specifically highlighting NAND and NOR, stating that any Boolean operation can be implemented using only these gates. The lecture transitions into the specific criteria required for a function to be considered functionally complete. The instructor emphasizes that a function must be able to implement the NOT operation along with either the AND or OR operation. Crucially, he notes a constraint that the function cannot rely on external support of constants (0 or 1) or pre-complemented variables to achieve this. The session concludes with a detailed walkthrough of a GATE 2015 exam problem, where the instructor analyzes two specific three-variable Boolean functions, f and g, to determine their functional completeness through variable substitution.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a slide titled "Functionally Complete Function" presented by Sanchit Jain Sir. The instructor explains that there are only three fundamental Boolean operators: NOT, AND, and OR, with all others derived from them. He points out that NOT along with OR (forming NOR) and NOT along with AND (forming NAND) are used as universal gates. The slide text explicitly states, "Any Boolean operation or function can be implemented with NAND or NOR operation." The instructor gestures towards the text, emphasizing that these two gates are sufficient to build any digital circuit.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to the whiteboard to define the conditions for functional completeness. He writes, "If any function can implement NOT along with it either AND or OR then, we indirectly prove that the function can also implement any other function, so function can said to be functionally complete." He adds a critical constraint: "Support of 0, 1 or complemented form of variables are not allowed." To illustrate, he writes a function f(a, b) = a' + b and evaluates it under different inputs, such as f(a, a) = 1 and f(a, 0) = a', demonstrating how to test for basic operations. He draws arrows connecting the function to NAND and NOR concepts.

  3. 5:00 – 7:17 05:00-07:17

    The final segment focuses on a specific problem from GATE 2015. The slide displays two functions: f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X, Y, Z) = X'YZ + X'YZ' + XY. The instructor analyzes f by substituting x, x, x into the equation, deriving f(x, x, x) = x', which proves it can implement NOT. He then analyzes g by substituting x, x, y, deriving g(x, x, y) = x + y, proving it can implement OR. The slide lists multiple-choice options (A, B, C, D) regarding the functional completeness of these functions. This practical application solidifies the theoretical concepts discussed earlier.

The lecture effectively bridges theory and practice. It starts by defining the building blocks of digital logic (NOT, AND, OR) and identifying NAND and NOR as the universal set. It then rigorously defines functional completeness, stressing the independence from external constants. Finally, it applies these rules to a complex exam problem, showing students exactly how to test a function's completeness by substituting variables to isolate fundamental operations like NOT and OR. This progression ensures students understand not just the definition, but the method of verification required for competitive exams like GATE.

Loading lesson…