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The prime implicant which has at least one element that is not present in any other implicant is known as ___________
- a)Essential Prime Implicant
- b)Implicant
- c)Complement
- d)Prime Complement
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The prime implicant which has at least one element that is not present...
Essential prime implicants are prime implicants that cover an output of the function that no combination of other prime implicants is able to cover.
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The prime implicant which has at least one element that is not present...
Essential Prime Implicant
The correct answer is option 'A', Essential Prime Implicant.
Explanation:
In digital logic design, a prime implicant is a product term that includes all the variables of a Boolean function in its minterm form. In other words, a prime implicant is a minimal expression that covers as many minterms as possible while still being valid.
Implicant:
An implicant is a product term that covers one or more minterms of a Boolean function. It can be a prime implicant or a non-prime implicant.
Complement:
The complement of a Boolean function is the function obtained by interchanging the 1s and 0s in the truth table of the original function.
Prime Complement:
There is no such term as "Prime Complement" in digital logic design.
Essential Prime Implicant:
An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicant. In other words, it is a prime implicant that cannot be eliminated without losing the completeness of the Boolean function.
Importance of Essential Prime Implicants:
- Essential prime implicants are necessary for obtaining a minimal expression of a Boolean function.
- They ensure that all minterms are covered by the expression.
- Without essential prime implicants, the function may not be fully represented and may lead to incorrect results.
Conclusion:
The prime implicant which has at least one element that is not present in any other implicant is known as an Essential Prime Implicant. It is important for obtaining a minimal expression of a Boolean function and ensuring the completeness of the function.
The correct answer is option 'A', Essential Prime Implicant.
Explanation:
In digital logic design, a prime implicant is a product term that includes all the variables of a Boolean function in its minterm form. In other words, a prime implicant is a minimal expression that covers as many minterms as possible while still being valid.
Implicant:
An implicant is a product term that covers one or more minterms of a Boolean function. It can be a prime implicant or a non-prime implicant.
Complement:
The complement of a Boolean function is the function obtained by interchanging the 1s and 0s in the truth table of the original function.
Prime Complement:
There is no such term as "Prime Complement" in digital logic design.
Essential Prime Implicant:
An essential prime implicant is a prime implicant that covers at least one minterm that is not covered by any other prime implicant. In other words, it is a prime implicant that cannot be eliminated without losing the completeness of the Boolean function.
Importance of Essential Prime Implicants:
- Essential prime implicants are necessary for obtaining a minimal expression of a Boolean function.
- They ensure that all minterms are covered by the expression.
- Without essential prime implicants, the function may not be fully represented and may lead to incorrect results.
Conclusion:
The prime implicant which has at least one element that is not present in any other implicant is known as an Essential Prime Implicant. It is important for obtaining a minimal expression of a Boolean function and ensuring the completeness of the function.
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