Basics of Number System Part-2

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: 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
  10. 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
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
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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