Half Subtractor

Duration: 11 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-subtractor 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 Half Subtractor, a fundamental combinational logic circuit used for binary subtraction. The instructor begins by defining the concept as the simplest form of subtracting two single-bit binary numbers, identifying four elementary operations. A key distinction is made regarding the case where a borrow is required (when Minuend=0 and Subtrahend=1). The lesson progresses to defining the circuit's inputs (A: Minuend, B: Subtrahend) and outputs (D: Difference, B: Borrow). The instructor then develops a truth table for all input combinations and derives the corresponding Boolean expressions using minterms. The Difference output is simplified to an XOR function (D = A ⊕ B), while the Borrow output is expressed as D = A'B. Finally, the instructor begins mapping these expressions to a logic circuit diagram using an XOR gate and an AND gate.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the Half Subtractor as a combinational logic circuit for subtracting two single-bit binary numbers. On-screen text lists the four elementary operations, specifically highlighting that a borrow is required when the minuend bit is 0 and the subtrahend bit is 1. The instructor writes binary subtraction equations on the whiteboard, including '0 - 0 = 0', '1 - 0 = 1', and '1 - 1 = 0'. The slide explicitly defines the inputs as A (Minuend) and B (Subtrahend), with outputs for Difference (D) and Borrow (B).

  2. 2:00 – 5:00 02:00-05:00

    The instructor transitions to a visual representation of the circuit by drawing green boxes on the whiteboard. A block diagram is created and labeled 'Half Subtractor (A-B)', with input arrows marked A and B leading to the box. The instructor then draws a truth table on the board, establishing headers for 'Inputs' (A, B) and 'Outputs' (D, B). This section focuses on the structural definition of the circuit before moving into logical derivation.

  3. 5:00 – 10:00 05:00-10:00

    The instructor completes the truth table by filling in the 0/1 rows for all input combinations. Using minterm notation, he derives the Boolean expressions: D(A,B) = Σm(1,3) and B(A,B) = Σm(1). The Difference expression is simplified to A'B + AB', which the instructor identifies as the XOR operation (D = A ⊕ B). The Borrow expression is simplified to A'B. The instructor then begins drawing the logic circuit diagram, starting with an XOR gate for the Difference output.

  4. 10:00 – 10:47 10:00-10:47

    The instructor reviews the completed logic design, pointing to the handwritten equations on the board. The final expressions are clearly visible: 'D = A ⊕ B' and 'B = ĀB'. The instructor gestures toward the truth table and the circuit components, reinforcing the relationship between the binary subtraction operations and their corresponding logic gate implementations.

The lecture follows a standard digital design progression: from arithmetic definition to logical implementation. The core takeaway is that the Half Subtractor requires two distinct logic functions: an XOR gate for the Difference and an AND gate (with one inverted input) for the Borrow. The instructor emphasizes that while most binary subtractions are straightforward, the 0-1 case necessitates a borrow from a higher-order bit. This circuit serves as the building block for more complex subtractors like the Full Subtractor.

Loading lesson…