Full Subtractor

Duration: 33 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-full-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, राज्य विशेष सामान्य ज्ञान / State-Specific 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, Git & Github, PHP
  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, Internet of Things
  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 full subtractor as a combinational logic circuit that performs arithmetic subtraction of three input bits: A (minuend), B (subtrahend), and B_{n-1} (borrow-in from the previous lower-significant position). The instructor begins with a slide definition and then uses a 4-bit binary example, A = 0110 and B = 1001, to motivate the need for borrow propagation. He labels MSB and LSB positions, highlights the least significant bit where a borrow is required (e.g., 10 - 1 = 1), and shows how subtraction proceeds bit by bit. A block diagram is drawn with inputs A, B, Bin and outputs D (difference) and Bout (borrow-out). The lecture then extends this to a multi-bit subtractor by cascading four full-subtractor stages labeled 0 through 3, with A = A3 A2 A1 A0 and B = B3 B2 B1 B0, showing how the borrow output of one stage feeds the borrow input of the next. A truth table is constructed with inputs A, B, Bin and outputs D, B (borrow), filled row by row using binary subtraction rules. From the truth table, minterm sums are written: D(A,B,Bin) = Σm(1,6,4,7) and B(A,B,Bin) = Σm(1,4,3,7). Finally, Boolean algebra simplification yields the standard full-subtractor equations: D = A ⊕ B ⊕ Bin and Bout = ĀB + (A ⊕ B)Bin. A final logic-gate diagram is drawn using XOR and OR gates to implement these expressions, completing the design of the full subtractor.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The lecture opens with a slide titled 'Full Subtractor' stating that it 'performs the arithmetic subtraction of three input bits.' The inputs are listed as A (Minuend) and B (Subtrahend), with a note that B_{n-1} represents the borrow from the previous lower-significant position. The instructor turns to the whiteboard and writes '(A - B)' followed by 'A = 0110' over 'B = 1001', setting up a concrete binary subtraction example to motivate the circuit design.

  2. 2:00 – 5:00 02:00-05:00

    The instructor explains the roles of minuend A, subtrahend B, and borrow-in Bin. He labels MSB and LSB on the board and walks through the subtraction example bit by bit, focusing on the least significant column where a borrow is needed. He writes '10 - 1 = 1' to demonstrate the borrow scenario and begins laying out a column subtraction with A and B rows under bit positions 3, 2, 1, 0.

  3. 5:00 – 10:00 05:00-10:00

    The instructor draws a green block diagram labeled 'Full Subtractor' with input arrows A, B, Bin and output arrows D and Bout, captioned 'Block Diagram.' He then extends this to a multi-bit representation, writing MSB: A3 A2 A1 A0 and LSB: B3 B2 B1 B0, and shows how the borrow input propagates through each bit position. He writes subtraction equations for individual bits, such as A0 - B0 = D0 and A1 - B1 - Bin1.

  4. 10:00 – 15:00 10:00-15:00

    The instructor builds a cascaded multi-bit subtractor by drawing red full-subtractor boxes. He starts with one box for bit 0 (inputs A0, B0, Bin0; output D0) and then adds a second box for bit 1 (inputs A1, B1, Bin1), showing how the borrow-out of one stage connects to the borrow-in of the next. The board also retains the '10 - 1 = 1' example and MSB/LSB labels as reference.

  5. 15:00 – 20:00 15:00-20:00

    The instructor completes the four-stage cascade, labeling boxes 'Full Subtractor (3)', '(2)', '(1)', and '0', with A = A3 A2 A1 A0 and B = B3 B2 B1 B0. He then transitions to logic design by drawing a green truth-table grid with column headers 'Inputs' (A, B, Bin) and 'Outputs' (D, B), beginning to fill in rows with 0s and dashes as he evaluates each combination.

  6. 20:00 – 25:00 20:00-25:00

    The instructor fills in the full truth table for the full subtractor, using binary subtraction rules such as '1 - 1 = 0' and lines beginning with '10 - 1' to determine output values for each input combination. Below the table, he writes minterm sums in pink: 'D(A,B,Bin) = Σm(1,6,4,7)' and 'B(A,B,Bin) = Σm(1,4,3,7)', identifying which input combinations produce a difference of 1 and a borrow-out of 1 respectively.

  7. 25:00 – 30:00 25:00-30:00

    The instructor applies Boolean algebra to simplify the minterm expressions. He shows steps for the borrow output, writing '= Bin(ĀA + AĀ) + ĀB' and then simplifying to '= ĀB + (A ⊕ B)Bin'. He also derives the difference output as 'D = A ⊕ B ⊕ Bin', using XOR identities to reduce the expressions to their minimal forms.

  8. 30:00 – 32:35 30:00-32:35

    The instructor draws the final logic-gate implementation of the full subtractor. He uses XOR gates to compute A ⊕ B and then (A ⊕ B) ⊕ Bin for the difference output D, and combines an AND gate with ĀB and (A ⊕ B)Bin fed into an OR gate for the borrow output Bout. The completed circuit diagram shows inputs A, B, Bin leading to outputs D and Bout, concluding the design.

The lecture follows a structured progression from motivation to implementation. It begins with the definition of a full subtractor and a concrete 4-bit binary example (A = 0110, B = 1001) to illustrate why borrow propagation is necessary. The instructor then abstracts this into a single-bit block diagram with inputs A, B, Bin and outputs D, Bout, before extending to a four-stage cascaded architecture for multi-bit subtraction. The core of the lecture is the truth-table construction, where all eight input combinations are evaluated using binary subtraction rules. From this table, minterm sums are extracted for both outputs: D = Σm(1,6,4,7) and Bout = Σm(1,4,3,7). Boolean algebra simplification then yields the canonical full-subtractor equations: D = A ⊕ B ⊕ Bin and Bout = ĀB + (A ⊕ B)Bin. The final gate-level diagram uses two XOR gates, one AND gate, and one OR gate to implement these expressions. Key takeaways for exam revision: (1) A full subtractor has three inputs and two outputs; (2) the difference output is a triple XOR of A, B, and Bin; (3) the borrow-out depends on both ĀB and the XOR of A and B multiplied by Bin; (4) multi-bit subtraction is achieved by cascading full subtractors with borrow chaining.

Loading lesson…