static hazard

Duration: 3 min

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Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: 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, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | 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, Hardware basics
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research
  19. GS Paper | 05 | Elementary Maths: संख्या पद्धति / Number System, Divisibility Rules, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, प्रतिशत / Percentage, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, समय और कार्य / Time and Work, समय, चाल और दूरी / Time, Speed and Distance, Algebra, घन क्षेत्रमिति / Solid Mensuration, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), मिश्रण और एलिगेशन / Mixture and Alligation, Calculus, Trigonometry, Vectors, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, यूक्लिडीय ज्यामिति और क्षेत्रमिति / Euclidean Geometry and Mensuration, सांख्यिकी और प्रायिकता / Statistics and Probability, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers, समतल क्षेत्रमिति / Plane Mensuration, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: समसामयिकी / Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The user wants a JSON summary of the provided video lecture. **1. Analyze the Video Content:** * **Topic:** Digital Logic Design, specifically Boolean functions, Karnaugh Maps (K-maps), and Static Hazards. * **Problem Statement:** The video starts with a question: "The Boolean function f(A, B, C, D) = Σm(2, 3, 5, 6, 7, 13) is implemented using its minimal SOP form. Will this circuit have any static hazard?" * **Methodology:** * The instructor draws a 4-variable K-map. * He labels the rows (AB) and columns (CD) with Gray code (00, 01, 11, 10). * He fills in the minterms: 2, 3, 5, 6, 7, 13. * He groups

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The user wants a JSON summary of the provided video lecture. **1. Analyze the Video Content:** * **Topic:** Digital Logic Design, specifically Boolean functions, Karnaugh Maps (K-maps), and Static Hazards. * **Problem Statement:** The video starts with a question: "The Boolean function f(A, B, C, D) = Σm(2, 3, 5, 6, 7, 13) is implemented using its minimal SOP form. Will this circuit have any static hazard?" * **Methodology:** * The instructor draws a 4-variable K-map. * He labels the rows (AB) and columns (CD) with Gray code (00, 01, 11, 10). * He fills in the minterms: 2, 3, 5, 6, 7, 13. * He groups the 1s to find the minimal Sum of Products (SOP) expression. * He identifies two groups: * Group 1: Minterms 2, 3, 6, 7. This corresponds to the term $\bar{A}C$. Wait, let me re-check the grouping. * Looking at the video around 0:20-0:30: * Minterms are at: * Row 00 (AB=00): Col 01 (2), Col 11 (3). * Row 01 (AB=01): Col 01 (5), Col 11 (7), Col 10 (6). Wait, 6 is at 0110. * Row 11 (AB=11): Col 01 (13). * Let's trace the groups drawn. * Group 1 (Green oval): Minterms 2, 3, 6, 7. * 2 (0010), 3 (0011), 6 (0110), 7 (0111). * Common variables: A=0, C=1. So term is $\bar{A}C$. * Group 2 (Green rectangle): Minterms 3, 7, 13... wait. * Let's look at the final expression written. * At 0:26, he writes $f(A,B,C,D) = \bar{A}C + B\bar{C}D$. * Let's check the groups for this. * $\bar{A}C$: Covers 2, 3, 6, 7. (Row 00 cols 11, 10? No. Row 00 is 0000-0011. Row 01 is 0100-0111. * Let's re-map the minterms carefully. * 2: 0010 (Row 00, Col 10). * 3: 0011 (Row 00, Col 11). * 5: 0101 (Row 01, Col 01). * 6: 0110 (Row 01, Col 10). * 7: 0111 (Row 01, Col 11). * 13: 1101 (Row 11, Col 01). * Okay, let's look at the groups drawn in the video. * Group 1 (Left oval): Covers 2, 3, 6, 7? No, looking closely at 0:20. * He circles 2, 3, 6, 7. Wait, 2 is 0010. 3 is 0011. 6 is 0110. 7 is 0111. * This group is $\bar{A}C$. * Group 2 (Right rectangle): Covers 3, 7, 13... wait. * He circles 3, 7, 13... and maybe 5? * Let's look at the final expression: $\bar{A}C + B\bar{C}D + \bar{A}BD$. * Wait, at 0:26 he writes $\bar{A}C + B\bar{C}D$. * Then at 0:28 he adds a redundant term $\bar{A}BD$ to remove the hazard. * Let's re-examine the groups. * Group 1: Minterms 2, 3, 6, 7. Term: $\bar{A}C$. * Group 2: Minterms 3, 7, 13... wait, 13 is 1101. 5 is 0101. * Let's look at the group for $B\bar{C}D$. * $B=1, C=0, D=1$. * Minterms: 0101 (5), 1101 (13). * So the group is 5 and 13. * So the minimal SOP is $\bar{A}C + B\bar{C}D$. * Wait, is 5 covered? Yes. Is 13 covered? Yes. * Is 2, 3, 6, 7 covered? Yes. * So minimal SOP is $f = \bar{A}C + B\bar{C}D$. * **Hazard Analysis:** * He checks for static hazards. A static-1 hazard occurs when two adjacent 1s are not covered by the same prime implicant. * He looks at the transition between the two groups. * Group 1 ($\bar{A}C$) covers 2, 3, 6, 7. * Group 2 ($B\bar{C}D$) covers 5, 13. * Are there adjacent 1s not covered by a single group? * Let's look at minterm 3 (0011) and minterm 2 (0010). Covered by $\bar{A}C$. * Let's look at minterm 3 (0011) and minterm 7 (0111). Covered by $\bar{A}C$. * Let's look at minterm 5 (0101) and minterm 7 (0111). * 5 is in group 2 ($B\bar{C}D$). * 7 is in group 1 ($\bar{A}C$). * They are adjacent (change in C). * Are they covered by a common group? No. * So there is a hazard between 5 and 7. * Let's look at minterm 13 (1101) and minterm 7 (0111). Not adjacent. * Let's look at minterm 13 (1101) and minterm 5 (0101). Covered by $B\bar{C}D$. * Let's look at minterm 13 (1101) and minterm 15 (1111). 15 is not a minterm. * Let's look at minterm 13 (1101) and minterm 9 (1001). 9 is not a minterm. * Let's look at minterm 13 (1101) and minterm 12 (1100). 12 is not a minterm. * Let's look at minterm 13 (1101) and minterm 5 (0101). Covered. * Wait, let's look at the transition between group 1 and group 2. * Group 1: $\bar{A}C$ (2, 3, 6, 7). * Group 2: $B\bar{C}D$ (5, 13). * Adjacent pairs: * (3, 7) - covered by $\bar{A}C$. * (2, 6) - covered by $\bar{A}C$. * (5, 13) - covered by $B\bar{C}D$. * (3, 2) - covered by $\bar{A}C$. * (7, 6) - covered by $\bar{A}C$. * (5, 7) - Adjacent (0101 vs 0111). 5 is in group 2, 7 is in group 1. No common group. **Hazard exists.** * (13, 15) - 15 is 0. * (13, 9) - 9 is 0. * (13, 12) - 12 is 0. * (13, 5) - covered. * (13, 11) - 11 is 0. * (13, 14) - 14 is 0. * (13, 9) - 9 is 0. * Wait, is there a transition between 13 and something else? * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110).

  2. 2:00 – 3:07 02:00-03:07

    14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list.

is not in list. * Let's check 13 (1101) and 14 (1110). 14 is not in list. * Let's check 13 (1101) and 5 (0101). Covered. * Let's check 13 (1101) and 11 (1011). 11 is not in list. * Let's check 13 (1101) and 15 (1111). 15 is not in list. * Let's check 13 (1101) and 9 (1001). 9 is not in list. * Let's check 13 (1101) and 12 (1100). 12 is not in list.

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