1's Complement Representation

Duration: 6 min

This video lesson is available to enrolled students.

Return to /learn/ISRO/digital-electronics/number-representation/basics-to-1s-complement/asset-1s-complement-representation after enrolling

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.

This educational video provides a comprehensive lecture on binary number systems, specifically focusing on Signed Magnitude, 1's Complement, and 2's Complement representations. The instructor begins by manually filling a comparison table for decimal numbers ranging from +7 to -8, demonstrating the bit patterns for each system. He then transitions to a theoretical slide explaining the range and conversion rules for 1's Complement, using +12 and -12 as a concrete example. Finally, the lesson covers number extension (sign extension), illustrating how to expand bit-widths for both positive and negative numbers while preserving their value and sign.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor is actively working on a large whiteboard table with columns labeled Decimal, Signed Magnitude, 1's Complement, and 2's Complement. He is writing binary values for positive integers starting from +7 down to +0. He points to specific rows, highlighting the bit patterns in the Signed Magnitude column where the most significant bit is 0. He is establishing the foundational binary representations for positive numbers before moving to the negative range, ensuring the audience understands the direct mapping of decimal to binary magnitude.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues filling the table, now focusing on negative numbers like -1, -2, and so on, drawing a horizontal line to separate positive and negative sections. He then switches to a slide titled '1's Complement Representation'. He writes the range formula $-(2^{n-1}-1)$ to $+(2^{n-1}-1)$ on the board. He demonstrates the conversion process by writing +12 as 01100 and then deriving -12 as 10011 by inverting the bits. He explains that the 1's complement is obtained by changing each 0 to 1 and each 1 to 0, effectively creating the negative counterpart.

  3. 5:00 – 6:27 05:00-06:27

    The lecture moves to a new topic titled 'Number extension'. The instructor explains that computer memory locations are fixed in size, requiring smaller numbers to be written in larger spaces. He draws rectangular boxes to represent bit positions. He illustrates that for positive numbers, extension is done by filling empty cells with 0s, similar to sign magnitude. For negative numbers, he demonstrates filling the empty cells with 1s to maintain the negative sign. He draws a specific example extending a 4-bit number to an 8-bit number, showing the padding of 1s on the left side for a negative value.

The video effectively bridges the gap between practical binary conversion and theoretical computer architecture concepts. It starts with the mechanical process of filling a conversion table to visualize how Signed Magnitude, 1's Complement, and 2's Complement differ. The instructor then formalizes these observations with the 1's Complement range formula and bit-inversion rules. The lesson concludes with the critical concept of sign extension, explaining how to preserve number integrity when changing bit-widths, a fundamental operation in digital logic and processor design. This progression from table-based examples to abstract rules and finally to architectural application provides a complete learning cycle for the topic.

Loading lesson…