Adding Two Unary Number

Duration: 6 min

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Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: 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, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. 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, Complexity Theory
  10. Compiler Design: 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
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a lecture on designing a Turing machine to perform addition of two numbers represented in unary notation. The instructor begins by stating the problem: given two unary numbers separated by a blank symbol, the machine must output their sum in unary. He illustrates the concept using a specific example where the input represents the numbers 3 and 4. The tape is initialized with a blank symbol, followed by three '1's, a separator 'B', four '1's, and trailing blanks. The goal is to transform this input into a sequence of seven '1's, representing the sum 7. The instructor then proceeds to design the state transition diagram step-by-step, explaining the logic behind each state and transition to achieve the desired result.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with the question "Design a Turing machine for addition of two number in unary?" displayed at the top. The instructor introduces the problem and begins drawing a tape diagram. He marks the start with 'B'. He writes three vertical lines '111' for the number 3. He places a 'B' as a separator. Next, he writes four vertical lines '1111' for the number 4. He labels the groups '3' and '4' above the tape. He explains the input is 111B1111. He states the output should be 1111111 (seven '1's). He emphasizes the machine must produce the correct unary sum.

  2. 2:00 – 5:00 02:00-05:00

    The instructor starts constructing the state diagram. He draws the initial state q0. He adds a self-loop on q0 labeled "1,1,R", indicating that the machine reads '1', writes '1', and moves right, staying in q0. This allows the machine to scan through the first number without changing it. He then draws a transition from q0 to a new state q1 labeled "B,1,R". He explains that when the machine encounters the separator 'B', it writes '1' and moves right. This effectively replaces the separator with a '1', merging the two numbers into a single block of '1's. Now the tape conceptually looks like 11111111. He draws state q1 and adds a self-loop "1,1,R" to scan through the second number. When it hits the end blank 'B', he draws a transition to state q2 labeled "B,B,L". This moves the head left to the last '1'. In state q2, he draws a transition to q3 labeled "1,B,R". He explains that this writes 'B' (deleting the '1') and moves right. This step removes the extra '1' that was added when the separator was replaced. Finally, from q3, he draws a transition to the final state q4 labeled "B,B,R".

  3. 5:00 – 5:31 05:00-05:31

    The instructor completes the state diagram by finalizing the transition to the final state q4. He briefly reviews the entire logic, confirming that the machine successfully adds the two numbers. He mentions that this approach works by effectively concatenating the numbers and then subtracting one to correct the count. He concludes the lecture segment, having successfully designed the Turing machine for unary addition. The video ends with the completed diagram visible on the screen, showing the states q0, q1, q2, q3, and q4 connected by the defined transitions.

The lecture demonstrates a systematic approach to designing a Turing machine for a basic arithmetic operation. By breaking down the problem into scanning, merging, and correcting steps, the instructor shows how simple state transitions can achieve complex tasks like addition. The key insight is treating the separator as a bridge to merge the unary strings and then adjusting the count to ensure accuracy. This method highlights the power of Turing machines in manipulating symbols on a tape to perform logical operations.

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