Adding Two Unary Number

Duration: 6 min

This video lesson is available to enrolled students.

Inside: a video lesson and guided study material.

Module outline

About Course: About the Course
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
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
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
AI, Machine Learning, Big Data & Cloud: Emerging Tech Trends, Artificial Intelligence, Big Data Systems, Approaches to AI, Search Algorithms, Knowledge Representation, Cloud Computing
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
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
Discrete Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic
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
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
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
Other Recurring CS Topics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, Multimedia
Live Classes: ISRO Live classes
Full Mock Test:

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

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.
2:00 – 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".
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.