Implicit Normalisation in Floating Point

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-SENIOR-COMPUTER-INSTRUCTOR/paper-2-fundamentals-of-computer/floating-point-rep/floating-point-basics/asset-implicit-normalisation-in-floating-point after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: 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: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- 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, Artificial Intelligence
  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: Child Development, Concept of Pedagogy, Psychology, Theories, Inclusive Education, Experiential Pedagogy, Curriculum Framework & Reforms, 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 video lecture covers the representation of decimal numbers in a custom floating-point format and introduces the theoretical basis for IEEE 754 standards. The instructor begins by solving a specific problem to represent -21.75 with 1 sign bit, 7 exponent bits, and 8 mantissa bits. He demonstrates the conversion of the decimal number to binary, normalization, and the calculation of the biased exponent. The lecture then transitions to a theoretical discussion on why floating-point representation is necessary for handling very large or small numbers, contrasting it with fixed-point limitations. Finally, the instructor introduces the IEEE 754 standard, explaining its role in standardizing floating-point arithmetic across different hardware implementations.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor reviews the representation of +21.75, showing binary 10101.11 and a biased exponent calculation resulting in 59 (1000101). He then transitions to the new problem: 'Represent -21.75 (s=1, k=7, m=8)'. He normalizes the number to 1.010111 x 2^4, sets the sign bit to 1, and calculates the new biased exponent as 64 + 4 = 68 (1000100). He pads the mantissa to 8 bits (01011100) and assembles the final bit pattern 1 1000100 01011100.

  2. 2:00 – 4:59 02:00-04:59

    The instructor discusses the limitations of fixed-point representation, stating on a slide that it 'do not works well if the number to be stored is either too small or too large'. He gives an example: 'Imagine a number 6.023 x 10^23 will require around 70 bits to be stored.' He introduces the biased exponent concept and displays two formulas: V = (-1)^S(M)_2 * 2^(E-Bias) (explicit) and V = (-1)^S(1.M)_2 * 2^(E-Bias) (implicit). He notes implicit representation has 'more precision than explicit normalization'. Finally, he introduces the 'IEEE 754 floating point standard', established in 1985, which addressed problems in diverse implementations to make hardware units reliable and portable.

The video effectively bridges practical calculation with theoretical standards. It begins with a hands-on example of encoding a negative decimal number into a custom floating-point format, demonstrating the steps of normalization, bias calculation, and bit assembly. This practical foundation leads into a theoretical discussion on why such representations are necessary for handling extreme values, contrasting fixed-point limitations with floating-point advantages. The lecture concludes by introducing the IEEE 754 standard, highlighting its role in standardizing arithmetic across hardware, thus providing a complete overview from manual encoding to industry standards.

Loading lesson…