Page Size

Duration: 10 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: UPPSC Course Overview
  2. Interview Preparation & Guidance: Interview Preparation
  3. Paper 1 | General 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, वर्णमाला, समास, संधि, 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), शब्द-भंडार, वर्ण-विचार, हिन्दी की ध्वनि और स्वनिम व्यवस्था, प्राचीन और मध्यकालीन भारतीय आर्यभाषाएँ, काव्य के लक्षण, हेतु और प्रयोजन, अशुद्धि-शोधन, शब्द-रचना, शब्द-भेद, हिन्दी की रूप रचना, रूप-रचना, हिन्दी शब्द रचना, हिन्दी साहित्येतिहास दर्शन, भक्तिकालीन काव्यधाराएँ, भारतीय काव्यशास्त्र की परंपरा, भारतीय नवजागरण और स्वाधीनता आंदोलन, अन्य गद्य विधाएँ एवं प्रवासी साहित्य, निर्धारित उपन्यासों का तुलनात्मक अध्ययन, गोदान, हिन्दी कहानी का विकास, स्वातंत्र्योत्तर और नयी कहानी, हिन्दी निबंध का विकास, शुक्लोत्तर निबंध, द्विवेदी और शुक्ल युग के निबंध, हिन्दी की संवैधानिक स्थिति, आधुनिक भारतीय आर्यभाषाएँ और हिन्दी का उद्भव, हिन्दी भाषा प्रयोग के विविध रूप, रीतिकाल, जीवनी, द्विवेदी युग और छायावाद, रीति, वक्रोक्ति और औचित्य सिद्धान्त, शब्दशक्ति और ध्वनि सिद्धान्त, रस सिद्धान्त और साधारणीकरण, उत्तर आधुनिकतावाद, लोहिया दर्शन, हिन्दी उपन्यास का विकास, हिन्दी नवजागरण, अंबेडकर दर्शन, आदिकाल, प्रयोगवाद और नयी कविता, छायावादी काव्य: प्रसाद और निराला, प्रगतिवाद से समकालीन कविता, निर्गुण भक्ति काव्य, द्विवेदीयुगीन काव्य, रीतिकालीन काव्य, आरंभिक हिन्दी उपन्यास, स्वातंत्र्योत्तर उपन्यास, आत्मकथा, स्वाधीनता-पूर्व प्रेमचंदोत्तर उपन्यास, निर्धारित कहानियों का तुलनात्मक अध्ययन, साठोत्तरी नाटक, प्रसाद और प्रसादोत्तर युग के नाटक, भारतेन्दु युगीन नाटक, स्वातंत्र्योत्तर नाटक, भारतेन्दु युगीन निबंध, संस्मरण और रेखाचित्र, व्यंग्य, एक साहित्यिक की डायरी, संस्कृति के चार अध्याय, सगुण भक्ति काव्य, हिन्दी नाटक, एकांकी और रंगमंच, आधुनिक गद्य और हिन्दी नवजागरण, अलंकार सिद्धान्त, हिन्दी आलोचना का विकास, भक्ति आंदोलन, कल्पना, बिम्ब, प्रतीक, मिथक और फंतासी, नयी कविता का विस्तार और साठोत्तरी कविता, उत्तर-छायावादी और प्रगतिवादी काव्य, काव्यगुण और काव्यदोष, प्लेटो, अरस्तू और पाश्चात्य परंपरा, मार्क्सवाद, स्वच्छन्दतावादी काव्यशास्त्र, आधुनिक पाश्चात्य आलोचना, भाषा और भाषा परिवार, देवनागरी लिपि
  4. Paper 2 | General Studies: State Wise GK, Polity, Geography, History, GK- Current Affairs
  5. Paper 1 | Programming Language: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  6. Paper 1 | Database Management Systems: 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, ORDBMS, NoSQL
  7. Paper 1 | Cyber Security: Society, Law & Ethics, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  8. Paper 1 | Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design
  9. Paper 1 | 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, Network Security
  10. Paper 1 | Design and Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  11. Paper 1 | Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  12. Paper 1 | Discrete Structures and Theory of Logic: Permutation and Combination, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  13. Paper 1 | Software Project Management: Software Project Management
  14. Paper 2 | Operating Systems: 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, Security
  15. 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  16. Paper 2 | Artificial Intelligence & High Performance Computing: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Natural Language Processing, Emerging Tech Trends
  17. Paper 2 | Image Processing: Digital Image Fundamentals, Image Enhancement, Image Restoration, Color Image Processing, Image Compression
  18. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  19. Paper 2 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  20. Paper 2 | Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, Java
  21. Paper 2 | Soft Computing: Fuzzy Sets, Artificial Neural Networks, Genetic Algorithms
  22. Paper 2 | Distributed System: Distributed Systems
  23. UPPSC Live Class Recordings: UPPSC Polytechnic Lecturer 2025 (CS)
  24. Previous Year Papers:
  25. Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture focuses on determining the optimal page size in operating systems to minimize total memory overhead. The instructor explains the trade-off between internal fragmentation and page table size. He defines variables for process size (x), page size (y), and page table entry size (z). He derives a cost function representing the sum of average internal fragmentation (y/2) and total page table size (xz/y). By differentiating this function with respect to page size (y) and setting it to zero, he derives the optimal page size formula: y = sqrt(2xz). The lecture begins by discussing the conflicting requirements: larger pages reduce the number of pages and thus the page table size, but increase the potential for wasted space within the last page. Conversely, smaller pages reduce waste but increase the overhead of managing more pages.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the topic "Size of Page" on a slide titled "Size of Page". He reads the bullet points which discuss the relationship between page size, internal fragmentation, and page table size. He notes that increasing the page size increases internal fragmentation but decreases the page table size, while decreasing the page size has the opposite effect. He defines three variables on the whiteboard: `Process size = x`, `Page size = y`, and `Page table entry = z`. He states the objective is to find the page size `y` where both costs (internal fragmentation and page table size) are minimal. He gestures towards the text on the slide to emphasize the trade-off. The slide text contains a typo, stating "If we increase the size of page table then internal fragmentation increase", but the instructor clarifies the intended meaning regarding page size. He explains that the goal is to balance these two opposing costs to find an optimal value.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins to visualize the problem by drawing a large rectangle representing the process size `x`. He divides this rectangle into smaller blocks representing pages of size `y`. He explains that the number of pages is `x/y`. He introduces the concept of internal fragmentation, stating that the maximum internal fragmentation is equal to the page size `y`, while the average internal fragmentation is `y/2`. He also defines the size of the page table as the number of pages multiplied by the size of a page table entry `z`, resulting in the formula `(x/y) * z`. He writes these components on the board to set up the cost function. He also writes down example values like `PS = 1KB` and `PI = 10B` to illustrate the concepts concretely. He draws lines inside the rectangle to show the division into pages, making the abstract concept of paging more tangible for the students.

  3. 5:00 – 10:00 05:00-10:00

    The instructor sets up the total cost equation by summing the average internal fragmentation and the total page table size: `Total Cost = (xz/y) + (y/2)`. To find the minimum cost, he differentiates this equation with respect to `y`. He writes the derivative as `d/dy (xz/y + y/2) = 0`. He calculates the derivative of the first term as `-xz/y^2` and the second term as `1/2`. Setting the sum to zero gives `-xz/y^2 + 1/2 = 0`. He rearranges the equation to solve for `y`, moving `xz/y^2` to the other side to get `1/2 = xz/y^2`. He then cross-multiplies to find `y^2 = 2xz`. Finally, he takes the square root to derive the optimal page size formula: `y = sqrt(2xz)`. He writes the final result clearly on the board. He explains that this formula gives the page size that minimizes the total overhead, balancing the cost of fragmentation against the cost of the page table.

  4. 10:00 – 10:12 10:00-10:12

    The instructor concludes the derivation by pointing to the final formula `y = sqrt(2xz)` written on the board. He emphasizes that this specific value for page size `y` minimizes the total overhead associated with memory management in a paging system. He reinforces that this mathematical result provides the theoretical optimal page size based on the process size and page table entry size. He gestures to the formula to ensure students understand the final takeaway of the lecture. He summarizes that this optimization is crucial for efficient memory utilization in operating systems.

The lecture provides a clear mathematical derivation for optimizing page size in operating systems. It starts by identifying the conflicting goals of minimizing internal fragmentation and minimizing page table size. By modeling these costs as functions of page size, the instructor uses calculus to find the equilibrium point. The final formula `y = sqrt(2xz)` serves as a practical guideline for system designers to balance memory efficiency against management overhead. This derivation is a classic example of applying mathematical optimization to computer science problems.

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