Basics of Number System Part-2

Duration: 7 min

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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 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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