Decimal to Any Base

Duration: 5 min

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Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. 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
  9. Paper 2 | 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
  10. Paper 2 | Databases: 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
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video features an instructor demonstrating the mathematical process of converting numbers between different bases. The specific problem presented is to convert the number $(4213.21)_5$ into base 7. The video shows an intermediate step where the base 5 number is first converted to decimal (base 10), resulting in $(558.44)_{10}$. The primary focus of the lecture is the second part of the conversion: transforming the decimal number $(558.44)_{10}$ into base 7. The instructor breaks down the problem into two distinct components: the integer part (558) and the fractional part (0.44). He uses a whiteboard to visually demonstrate the algorithms required for each part, ensuring students can follow the step-by-step arithmetic involved in changing number systems.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by writing the conversion problem on the whiteboard: $(4213.21)_5 ightarrow (558.44)_{10} ightarrow (\dots)_7$. He explicitly underlines the decimal number 558.44 to indicate this is the starting point for the current exercise. He starts with the integer part, 558. He sets up a long division format with 7 as the divisor and 558 as the dividend. He performs the division $558 \div 7$, calculating the quotient as 79 and the remainder as 5. He writes "79 - 5" on the board. He then proceeds to divide the quotient 79 by 7, obtaining a new quotient of 11 and a remainder of 2. This process continues with 11 divided by 7, yielding a quotient of 1 and a remainder of 4. Finally, he divides 1 by 7, resulting in a quotient of 0 and a remainder of 1. He reads the remainders from the last step upwards to form the integer part of the base 7 number, which is 1425.

  2. 2:00 – 4:32 02:00-04:32

    Next, the instructor addresses the fractional part of the decimal number, which is 0.44. He explains that for fractional parts, the method involves repeated multiplication by the target base, which is 7. He writes $0.44 imes 7$ and calculates the result as 3.08. He identifies the integer part, 3, as the first digit after the decimal point in the new base. He then takes the remaining fractional part, 0.08, and multiplies it by 7 to get 0.56. The integer part 0 becomes the next digit. He continues this iterative process: $0.56 imes 7 = 3.92$ (digit 3), $0.92 imes 7 = 6.44$ (digit 6), and $0.44 imes 7 = 3.08$ (digit 3). He writes these digits sequentially to form the fractional part $.30363$. Finally, he combines the integer and fractional results to write the final answer on the board as $(1425.30363)_7$.

The lecture effectively illustrates the standard algorithms for base conversion. For the integer portion, the repeated division method is used, where the remainders collected in reverse order form the digits of the new base. For the fractional portion, the repeated multiplication method is applied, where the integer parts collected in order form the digits of the new base. The instructor's clear step-by-step breakdown on the whiteboard helps visualize the arithmetic operations involved in changing number systems.

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