No of Function possible

Duration: 8 min

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  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: 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, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video lecture explains the mathematical derivation for determining the total number of possible Boolean functions given 'n' Boolean variables. The instructor begins by presenting the problem on a slide, stating that with n binary variables, there are $2^n$ possible input combinations. Since a Boolean function can only output two values (0 or 1), the total number of distinct functions is calculated as $2^{(2^n)}$. The lecturer then generalizes this concept using the notation $x^{(y^z)}$, where x represents the nature of the function, y represents the nature of the variable, and z represents the number of variables. He transitions to a whiteboard to illustrate this with a concrete example using two variables, 'a' and 'b', demonstrating how the 4 input combinations lead to 16 possible functions.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a slide titled 'No of functions possible'. The instructor poses the question: 'With n-Boolean variables how many different Boolean functions are possible?'. He reads the solution provided on the screen, explaining that n binary variables generate $2^n$ combinations. He notes that a Boolean function has only 2 possible values (0 or 1). Consequently, the total number of different functions possible is $2^{(2^n)}$. He introduces a generalized formula $x^{(y^z)}$ to represent this, defining x as the nature of the function, y as the nature of the variable, and z as the number of variables.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to a whiteboard to visualize the concept. He writes two variables, 'a' and 'b', and lists their 4 possible binary combinations: 00, 01, 10, and 11. He draws two ovals labeled 'A' and 'B' to represent the input and output sets. Inside 'A', he writes 'a', 'b', and '2' to indicate 2 variables. Inside 'B', he writes '1' and '2' to indicate 2 possible output values. He explains that for each of the 4 rows in the truth table, the output can be either 0 or 1. He begins drawing a truth table with columns labeled $f_1, f_2, f_3, f_4$ to show different function mappings, eventually concluding that there are 16 possible functions ($2^4$) for 2 variables.

  3. 5:00 – 8:02 05:00-08:02

    The instructor reinforces the generalization on the whiteboard. He writes 'nature of function -> 2' and 'nature of variable -> 2'. He writes the formula $2^{(2^n)}$ clearly. He explains the components: x (nature of function) is 2, y (nature of variable) is 2, and z (number of variables) is n. He writes examples like $2^{(2^3)}$ to show how the formula applies to 3 variables, solidifying the derivation of the total number of Boolean functions. He emphasizes that the base is the number of output values and the exponent is the number of input combinations.

The lecture provides a clear, step-by-step derivation of the formula for the number of Boolean functions. It starts with the fundamental property of binary variables ($2^n$ combinations) and combines it with the binary nature of the output (2 values) to arrive at the final formula $2^{(2^n)}$. The instructor effectively uses both slide text and whiteboard diagrams to bridge the gap between abstract formulas and concrete examples, specifically demonstrating the 16 functions possible with 2 variables before generalizing to 'n' variables using the notation $x^{(y^z)}$.

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