Partially complete Function

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/digital-electronics/boolean-expression/functional-completeness/asset-partially-complete-function after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. General Aptitude & Reasoning: Number System, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Speed Time and Distance, Mixture and Alligation, Data Interpretation, Algebra, Probability, Permutation and Combination, Venn Diagram, HCF LCM, Divisibility Rules, Age Problems, Pipe and Cistern, Partnership, Linear Algebra, Sequence and Series (Series), Statistics, Powers and Exponents (Surds and Indices), Arithmetic, Mensuration and Geometry, Calculus, Trigonometry, Vectors, Speed Mathematics and Basic Mathematics, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analogy, Series (Number and Letter Series) (Numerical Relations and Reasoning), Puzzle Solving (Puzzles), Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Calendar, Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Clock, Analytical Reasoning (Counting Figures Reasoning), Ranking, Order and Sequence, Logical Sequence Of Words, Inequality, Data Sufficiency, Cubes & Dices
  3. Computer Networks & Cybersecurity: 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, Network Security
  4. Programming, Data Structures & Algorithms: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  5. AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
  6. Digital Logic & Computer Organization: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. TOC & Compiler: 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, 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
  8. Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
  9. 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, Distributed Systems
  10. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Object Oriented Technology, HTML Basics, JavaScript-Basics, Java, XML
  11. Database Management System: 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, Data Warehousing & Mining, Enhanced Data Models, NoSQL
  12. Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
  13. Live Classes: ISRO Live classes
  14. Full Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture focuses on the digital logic concept of 'Partially Functionally Complete' functions. The instructor defines this property as the ability to implement any digital circuit using a specific function, with the constraint that logic 0 or 1 can be used as input lines, but complemented forms of inputs are not allowed. He uses the function f(a,b) = a' . b as a case study to demonstrate how to verify this property through algebraic manipulation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by writing the formal definition on the whiteboard: 'A function is said to be partially functionally complete, if it can be implement any digital circuit with support of logic 0 or 1 as a input line (can't use complemented form).' He introduces the specific function f(a,b) = a' . b and systematically evaluates it under different input conditions. He first checks f(a,a), which results in a' . a = 0. Next, he evaluates f(a,0), yielding a' . 0 = 0. Finally, he calculates f(a,1) = a' . 1 = a'. This last step is critical as it proves the function can generate a NOT gate (inverter) by simply tying one input to logic 1.

  2. 2:00 – 3:16 02:00-03:16

    Moving to the right side of the board, the instructor analyzes the nested expression f(f(a,1), b). He substitutes the previously derived result, replacing the inner f(a,1) with a'. This simplifies the expression to f(a', b). By applying the original definition f(x,y) = x' . y, he substitutes a' for the first variable, resulting in (a')' . b. The double negation cancels out, leaving a . b. This derivation proves that the function can implement an AND gate. Since the function can generate both NOT and AND operations, it satisfies the criteria for being partially functionally complete.

The lecture effectively bridges the gap between abstract definitions and practical circuit implementation. By breaking down the function f(a,b) = a' . b, the instructor demonstrates that partial functional completeness relies on the availability of constant inputs to generate fundamental logic gates like NOT and AND. This capability allows the construction of any complex digital circuit, provided the specific constraints regarding complemented inputs are respected. The step-by-step algebraic proof serves as a template for analyzing other functions for this property.

Loading lesson…