Orthogonal Function

Duration: 4 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
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  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
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  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
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  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
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  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.

The video lecture introduces the concept of orthogonal functions in Boolean algebra, defining them as functions where the complement (f') is equal to the dual (f^d). The instructor demonstrates this property using the XOR function, f = a'b + ab', showing that both its complement and dual simplify to the Ex-NOR function. The lecture also notes that a function cannot be simultaneously orthogonal and self-dual. The session concludes by transitioning to a new problem set asking students to identify which of the given minterm functions are self-dual.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by defining an orthogonal function with the on-screen text: 'A function f is said to be orthogonal if the compliment and dual of the function are same.' He writes the condition f' = f^d on the board. He also notes a property visible at the top: 'A function can never be both orthogonal and self-dual because it imply the function is same to its compliment, which is never possible.' To illustrate the definition, he writes the function f = a'b + ab' (XOR). He then calculates the dual by replacing AND with OR and OR with AND, resulting in (a'+b)(a+b'). Simultaneously, he calculates the complement using De Morgan's laws, which also results in (a+b')(a'+b). He labels both results as 'Ex-NOR' on the board, confirming that for this function, the complement equals the dual, thus making it orthogonal.

  2. 2:00 – 4:04 02:00-04:04

    After a 'Break' slide, the instructor presents a new question: 'Q which of the following functions are self-dual?' The slide lists four options involving minterm notation: f(a, b, c) = Σm(0, 3), F(a, b, c) = Σm(0, 1, 6, 7), F(a, b, c) = Σm(1, 2, 4), and F(a, b, c) = Σm(3, 5, 6, 7). The instructor stands by the board, preparing to explain the criteria for self-duality, which requires a function to be equal to its own dual (f = f^d). He gestures towards the options, indicating the start of a problem-solving session to determine which specific minterm combinations satisfy the self-dual condition.

The lesson progresses from defining orthogonal functions to applying the definition with a concrete XOR example, proving that its complement and dual are identical Ex-NOR expressions. It briefly establishes a theoretical constraint that orthogonal and self-dual properties are mutually exclusive. Finally, the lecture shifts focus to self-dual functions, presenting a multiple-choice question with minterm lists to test the student's ability to identify functions where f = f^d. The transition from theoretical definition to practical application marks the end of this segment.

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