static hazard

Duration: 3 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  3. Paper 2 | Computer Organization And Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Control Unit Design, Instr Formats & Modes, Programming the Basic Computer
  4. Paper 2 | Analog And Digital Communication: Introduction to Communication Systems & Random Signals, Analog Communication Systems, Information Theory & Digital Communication Fundamentals, Digital Modulation & Detection Techniques, Error Control, Synchronization & Multiple Access Techniques
  5. Paper 2 | Programming in C: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. Paper 2 | Data Structures And Programming: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  7. Paper 2 | Algorithms: Algorithm Analysis, Sorting Algorithms, Time Complexity Analysis, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  8. Paper 2 | 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
  9. Paper 2 | 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
  10. Paper 2 | Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  11. Paper 2 | Information Systems and Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Paper 2 | 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
  13. Paper 2 | Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, CSS, XML, HTML5
  14. Paper 2 | Cyber Security And Emerging Technologies: Emerging Tech Trends
  15. Paper 2 | Cloud Technology: Cloud Computing
  16. Paper 2 | Probability and statistics: Probability, Statistics
  17. Paper-1 English: Vocabulary, Preposition, Articles, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage), Sentence Construction
  18. Paper 1 General Mental Ability & Logical reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Powers and Exponents (Surds and Indices), Algebra, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Mental Ability, Age Problems, Partnership, Arithmetic, Speed Mathematics and Basic Mathematics, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Venn Diagram, Analogy
  19. Paper-1 General Knowledge & Current Affairs: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge
  20. Full Length Mock Test:
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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