static hazard

Duration: 3 min

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Module outline

  1. About Course: About the Course
  2. Paper 1 | General Studies: State Wise GK
  3. Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
  4. Paper 1 | Current Affairs: GK- Current Affairs
  5. Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Probability
  6. Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, 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
  7. Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  8. Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  9. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  10. Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
  11. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
  12. Paper 2 | 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
  13. 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
  14. Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
  15. Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, 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
  16. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Current Trends & Technologies: Emerging Tech Trends, Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Artificial Intelligence, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce, Terms & Abbreviations
  18. Paper 2 | Full Length Mock Tests:
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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