Basics of Number System Part-2

Duration: 7 min

This video lesson is available to enrolled students.

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: 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
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: 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, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture begins by introducing fundamental number systems used in computing and mathematics, specifically Binary, Octal, Hexadecimal, Unary, and Decimal. A table is displayed listing the "Base or Radix" and "Digits or symbols" for each system. The instructor then provides a formal definition of a number system as an ordered set of symbols ranging from 0 to r-1, where r is the base. He explains the structure of numbers containing both integer and fractional parts separated by a radix point. The session concludes with a detailed breakdown of the Decimal Number System, demonstrating how to expand a number into a sum of coefficients multiplied by powers of 10, using examples like 749.52 and 721.74 to illustrate the concept of weighted values.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor starts by displaying a comprehensive table comparing different number systems. The first section lists Binary (Base 2, digits 0,1), Octal (Base 8, digits 0-7), and Hexadecimal (Base 16, digits 0-9, A-F). He then points to a second table below it featuring Unary (Base 1, digits 0/1) and Decimal (Base 10, digits 0-9). He actively engages with the content by circling the base "10" for the Decimal system and "1" for the Unary system. He also writes "16" in the top right corner of the slide and points to the specific symbols used, emphasizing the range of digits available in each system.

  2. 2:00 – 5:00 02:00-05:00

    The lecture moves to a text-based slide defining a number system formally. The text states it is an ordered set of symbols called digits, from 0 to r-1, if r is the base or radix. The instructor writes "(0 1 2 ... 9)10" on the screen to visualize the digit range for base 10. He emphasizes the rule that one cannot use a digit higher than r-1 in base r. He then introduces the general mathematical representation of a number with a decimal point: $(a_{n-1} a_{n-2} ... a_1 a_0 . a_{-1} a_{-2} ... a_{-m})$. He writes "749.52" as a practical example and draws brackets to separate the integer part from the fractional part, explaining the role of the radix point.

  3. 5:00 – 6:51 05:00-06:51

    The final segment focuses specifically on the Decimal Number System. A slide explains that it is a base-10 system using ten digits (0-9) where coefficients are multiplied by powers of 10. The instructor provides an example $(7,392)_{10}$ and expands it into $7 * 10^3 + 3 * 10^2 + 9 * 10^1 + 2 * 10^0$. He then generalizes this for numbers with decimal points, writing "721.74" on the board. He expands this number into $7*10^2 + 2*10^1 + 1*10^0 + 7*10^{-1} + 4*10^{-2}$. Finally, he calculates the individual terms ($700 + 20 + 1 + 0.7 + 0.04$) to show how they sum back to the original number, reinforcing the concept of positional weighting.

The video serves as an introductory lesson on number systems, establishing the relationship between a base and its available digits. It progresses from a comparative overview of common systems like Binary and Hexadecimal to a formal definition involving the variable 'r' for base. The core pedagogical goal is to teach the concept of positional notation, where the value of a digit is determined by its position relative to the radix point. This is solidified through the detailed expansion of decimal numbers, showing how integer and fractional parts correspond to positive and negative powers of the base, respectively.

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