Half Adder

Duration: 8 min

This video lesson is available to enrolled students.

Return to /learn/BIHAR-STET-COMPUTER-SCIENCE-COMPLETE-COURSE/unit-1-digital-electronics/combinational-circuit/adders-subtractors/asset-half-adder after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the course: About the Course
  2. Mathematical Aptitude: संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Divisibility Rules, प्रतिशत / Percentage, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, लाभ, हानि और बट्टा / Profit, Loss and Discount, समय और कार्य / Time and Work, घन क्षेत्रमिति / Solid Mensuration, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, समय, चाल और दूरी / Time, Speed and Distance, Age Problems, मिश्रण और एलिगेशन / Mixture and Alligation, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, Pipe and Cistern, Trigonometry, Statistics, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Logical Reasoning: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, सादृश्यता एवं वर्गीकरण / Analogy and Classification, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, क्रम एवं रैंकिंग / Order and Ranking, अशाब्दिक तर्क / Non-Verbal Reasoning, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, Syllogisms, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Analytical Reasoning (Counting Figures Reasoning), घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, कैलेंडर एवं घड़ी / Calendar and Clock, Clock
  4. General Knowledge: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Chemistry, Biology, History, Geography, Polity, Indian Economy, समसामयिकी / Current Affairs, Static General Knowledge
  5. Art of Teaching: शिक्षण-अधिगम प्रक्रिया एवं कक्षा प्रबंधन / Teaching-Learning Process and Classroom Management, Learners & Learning Process, Factors Affecting Teaching, शिक्षण विधियाँ एवं उपागम / Teaching Methods and Approaches, सूक्ष्म शिक्षण एवं कक्षा संप्रेषण / Microteaching and Classroom Communication, शिक्षण सहायक सामग्री एवं शैक्षिक तकनीकी / Teaching Aids and Educational Technology, आकलन एवं मूल्यांकन / Assessment and Evaluation, शिक्षक: गुण, व्यावसायिक नैतिकता एवं विकास / Teacher: Qualities, Professional Ethics and Development, शैक्षिक नीतियाँ, अधिनियम एवं प्रशासन / Educational Policies, Acts and Administration, पाठ्यचर्या, कला एवं सह-शैक्षिक क्षेत्र / Curriculum, Arts and Co-curricular Areas, निर्देशन एवं परामर्श / Guidance and Counselling, दिव्यांग बच्चों की शिक्षा / Education of Children with Disabilities, Micro-Teaching & Teaching Skills, पाठ योजना / Lesson Planning
  6. Environmental Science: Environment
  7. Unit 1 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  8. Unit 2 | COA: Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Programming the Basic Computer
  9. Unit 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  10. Unit 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  11. Unit 4 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  12. Unit 5 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  13. Unit 6 | 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, Transaction Management, Concurrency Control
  14. Unit 7 | 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
  15. Unit 8 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  16. Unit 9 | Object Oriented Programming: OOPS with C++
  17. Unit 10 | Web Development: HTML Basics, CSS, JavaScript-Basics, XML, Node.js
  18. Unit 11 | 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
  19. Unit 12 | IoT: Emerging Tech Trends, Cloud Computing, कंप्यूटर नेटवर्क / Computer Networks
  20. Unit 13 | Artificial Intelligence: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms
  21. Unit 14 | E-Commerce: Electronic Data Interchange and E-Commerce, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Physical Security and Cryptography Basics, Cyber Safety and Security
  22. Unit 15 | Multimedia: Multimedia
  23. Unit 16 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  24. Full Length Mock Tests — General Paper:
  25. Full Length Mock Tests — Computer Science (Paper II):
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces the fundamental building blocks of digital arithmetic, specifically focusing on the Half Adder. The instructor begins by explaining the necessity of hierarchical design in circuit development, moving from simple half adders to full adders and finally to n-bit adders. To clarify the concept of "carry," he uses a base-9 addition example (768 + 557), demonstrating how remainders and quotients work in different bases. The lesson then transitions to binary logic, outlining the four elementary addition operations. The core of the lecture defines the Half Adder circuit, detailing its inputs (A, B) and outputs (Sum, Carry), and presents its truth table and corresponding logic gate implementation using XOR and AND gates.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a slide titled "Why we need a half adder". The text defines a binary adder-subtractor as a combinational circuit performing arithmetic operations. The instructor explains the hierarchical design approach, stating, "The half adder design is carried out first, from which we develop the full adder." He writes "Basics of addition: (A)x + (B)x = ?" on the screen. To illustrate the concept of carry, he sets up an addition problem in base 9: 768 + 557. He explains that in base 9, digits range from 0 to 8. He begins the calculation by adding the rightmost digits, 8 and 7. He notes that 8 + 7 equals 15 in decimal. Since the base is 9, he explains that 15 divided by 9 gives a quotient of 1 and a remainder of 6. This sets up the concept of carrying over a value to the next significant bit, which is fundamental to digital addition. He writes the remainder 6 at the bottom and carries the 1.

  2. 2:00 – 5:00 02:00-05:00

    Continuing the base 9 example, the instructor calculates the middle column: 6 + 5 plus the carry of 1. This sums to 12 in decimal. In base 9, 12 is represented as 13 (1 carry, 3 remainder). He writes the carry '1' above the next column. Finally, he adds the leftmost column: 7 + 5 plus the carry of 1, which equals 13 in decimal. In base 9, this is 14. The final result is written as 1436. The instructor then transitions to binary addition. A new slide appears titled "Half adder". It lists the four elementary operations: 0+0=0, 0+1=1, 1+0=1, and 1+1=10. He emphasizes that the first three operations produce a single digit sum, but 1+1 produces a two-digit result (10 binary), where the higher significant bit is called a carry. This distinction is crucial for understanding how digital circuits handle overflow. He writes the binary addition table on the board, showing 0+0, 0+1, 1+0, and 1+1.

  3. 5:00 – 8:23 05:00-08:23

    The lecture formally defines the Half Adder. The slide states it is a combinational circuit that performs the arithmetic addition of two one-bit binary numbers. The inputs are labeled A and B, and the outputs are Sum (S) and Carry (C). The instructor fills out the truth table: for inputs 0 and 0, Sum is 0 and Carry is 0. For 0 and 1, Sum is 1 and Carry is 0. For 1 and 0, Sum is 1 and Carry is 0. For 1 and 1, Sum is 0 and Carry is 1. He then displays the logic circuit diagram. The Sum output is generated by an XOR gate, while the Carry output is generated by an AND gate. He points out that this circuit has no provision for a carry coming from a previous stage. The final frame shows a block diagram of a 4-bit adder, illustrating how multiple adders are connected in cascade to handle multi-bit numbers, labeled A(A3 A2 A1 A0) and B(B3 B2 B1 B0). He gestures towards the carry lines connecting the stages.

The video provides a comprehensive introduction to digital arithmetic circuits, logically progressing from general concepts to specific implementations. By using a base-9 example, the instructor effectively demystifies the concept of "carry" before applying it to binary logic. The lesson culminates in defining the half adder's truth table and logic gates, setting the stage for more complex circuits like the full adder and n-bit adders. This structured approach ensures students understand the underlying mechanics of binary addition before moving to circuit design.

Loading lesson…