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Directions: Consider the following statements.
- Boolean expressions and logic networks correspond to labelled acyclic digraphs.
- Optimal boolean expressions may not correspond to simplest networks.
- Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.
Which of these statement(s) is/are correct?
- a)1 only
- b)2 only
- c)1 and 2
- d)1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Directions: Consider the following statements. Boolean expressions and...
Statement 1: Boolean expressions and logic networks correspond to labelled acyclic digraphs.
Boolean expressions can be represented using logic networks, which are composed of logic gates such as AND, OR, and NOT gates. These logic networks can be represented as labelled acyclic digraphs, where each gate is represented as a node and the connections between gates are represented as directed edges.
This statement is correct because boolean expressions and logic networks are closely related and can be represented using labelled acyclic digraphs.
Statement 2: Optimal boolean expressions may not correspond to simplest networks.
In boolean logic, an optimal expression is one that requires the fewest number of gates or operations to implement a given logic function. However, this does not necessarily mean that the corresponding logic network will be the simplest.
There are various factors to consider when designing a logic network, such as the cost of different types of gates, the physical space available for implementation, and the desired speed or performance. These factors may lead to a design that is not the simplest in terms of gate count, but still achieves the desired functionality.
This statement is correct because simplicity in terms of gate count may not always be the primary concern when designing optimal boolean expressions.
Statement 3: Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.
A Karnaugh map is a graphical representation of a truth table, where adjacent cells in the map differ by only one variable. It is often used to simplify boolean expressions by identifying groups of adjacent cells that can be combined into larger blocks.
Choosing essential blocks first means identifying and covering the cells in the Karnaugh map that correspond to the required logic function. Greedily choosing the largest remaining blocks involves selecting the largest groups of adjacent cells that have not been covered yet.
However, this approach may not always result in an optimal expression because it does not consider all possible combinations of adjacent cells. There may be other groupings that result in a smaller boolean expression, but they are not considered when using a greedy approach.
This statement is correct because the greedy approach of selecting the largest remaining blocks may not always lead to the smallest possible boolean expression.
Therefore, all three statements are correct.
Boolean expressions can be represented using logic networks, which are composed of logic gates such as AND, OR, and NOT gates. These logic networks can be represented as labelled acyclic digraphs, where each gate is represented as a node and the connections between gates are represented as directed edges.
This statement is correct because boolean expressions and logic networks are closely related and can be represented using labelled acyclic digraphs.
Statement 2: Optimal boolean expressions may not correspond to simplest networks.
In boolean logic, an optimal expression is one that requires the fewest number of gates or operations to implement a given logic function. However, this does not necessarily mean that the corresponding logic network will be the simplest.
There are various factors to consider when designing a logic network, such as the cost of different types of gates, the physical space available for implementation, and the desired speed or performance. These factors may lead to a design that is not the simplest in terms of gate count, but still achieves the desired functionality.
This statement is correct because simplicity in terms of gate count may not always be the primary concern when designing optimal boolean expressions.
Statement 3: Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.
A Karnaugh map is a graphical representation of a truth table, where adjacent cells in the map differ by only one variable. It is often used to simplify boolean expressions by identifying groups of adjacent cells that can be combined into larger blocks.
Choosing essential blocks first means identifying and covering the cells in the Karnaugh map that correspond to the required logic function. Greedily choosing the largest remaining blocks involves selecting the largest groups of adjacent cells that have not been covered yet.
However, this approach may not always result in an optimal expression because it does not consider all possible combinations of adjacent cells. There may be other groupings that result in a smaller boolean expression, but they are not considered when using a greedy approach.
This statement is correct because the greedy approach of selecting the largest remaining blocks may not always lead to the smallest possible boolean expression.
Therefore, all three statements are correct.
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Community Answer
Directions: Consider the following statements. Boolean expressions and...
- Boolean expressions and logic networks correspond to labelled acyclic digraphs. Correct
- Optimal boolean expressions may not correspond to simplest networks. Correct
- Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression. Correct
So, option (4) is correct.
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Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?
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Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer?.
Solutions for Directions: Consider the following statements. Boolean expressions and logic networks correspond to labelled acyclic digraphs. Optimal boolean expressions may not correspond to simplest networks. Choosing essential blocks first in a Karnaugh map and then, greedily choosing the largest remaining blocks to cover may not give an optimal expression.Which of these statement(s) is/are correct?a)1 onlyb)2 onlyc)1 and 2d)1, 2 and 3Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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