Question

The Prime Implicant (PI) whose each 1 is covered by a minimum of one Essential Prime Implicant (EPI) is known as:

• A. Essential prime implicant
• B. Selective prime implicant
• C. False prime implicant
• D. Redundant prime implicant

Hint:

Essential Prime Implicants are critical for covering all the 1's in a Boolean expression and are a key part of simplification.

Answer 1

The Correct Option is A

Step 1: Define Essential Prime Implicant (EPI).
An Essential Prime Implicant (EPI) is a prime implicant that covers a minterm not covered by any other prime implicant.

Step 2: Clarify Prime Implicant Definition.
An Essential Prime Implicant (EPI) is a prime implicant where every minterm it covers is also covered by at least one other prime implicant. This implies that the minterms covered by an EPI are uniquely handled by it, and cannot be covered by any other implicant.

Step 3: Evaluate Options.
- (A) Essential prime implicant: This is correct. The definition provided aligns with the description of an EPI. - (B) Selective prime implicant: This is incorrect. This term is not used to describe prime implicants covered by EPIs. - (C) False prime implicant: This is incorrect. False implicants do not meet the required conditions for covering minterms. - (D) Redundant prime implicant: This is incorrect. Redundant implicants are not critical for the minimization process.

Step 4: Conclusion.
The correct answer is (A) Essential prime implicant, as it accurately reflects the definition provided in the question.