Consider the following statements: (a) Boolean expressions and logic gates…
2015
Consider the following statements:
(a) Boolean expressions and logic gates networks correspond to labelled acyclic digraphs
(b) Optimal boolean expressions may not correspond to simplest networks.
(c) 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.
(a) only
- B.
(b) only
- C.
(a) and (b)
- D.
(a), (b) and (c)
Attempted by 93 students.
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Correct answer: D
Answer: The correct answer is Option D because all three statements accurately reflect the theoretical and practical nuances of digital logic design. Statement (a) correctly defines combinational circuits as Directed Acyclic Graphs (DAGs) in graph theory. Statement (b) validly distinguishes between mathematical optimization (minimizing literals) and hardware efficiency (minimizing gate count), noting they are not always identical. Finally, Statement (c) correctly identifies a known algorithmic limitation where "greedy" selection in K-maps fails to find the true minimum in specific cyclic scenarios (requiring advanced methods like Petrick's Method). Therefore, every statement provided is valid.