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A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:
F = A̅.B̅.C̅ + A̅.B.C̅ + A.B̅.C̅
where, A̅, B̅, and C̅ are the complements of the respective variables. The product of sums (POS) form of the function F is
F = A̅.B̅.C̅ + A̅.B.C̅ + A.B̅.C̅
where, A̅, B̅, and C̅ are the complements of the respective variables. The product of sums (POS) form of the function F is
- a)F = (A + B + C) . (A + B̅ + C) . (A̅ + B + C)
- b)F = (A̅ + B̅ + C̅) . (A̅ + B + C̅) + (A + B̅ + C̅)
- c)F = (A + B + C̅) . (A + B̅ + C̅) . (A̅ + B + C̅) . (A̅ + B̅ + C) . (A̅ + B̅ + C̅)
- d)F = (A̅ + B̅ + C) . (A̅ + B + C) . (A + B̅ + C) . (A + B + C̅) . (A + B + C)
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A function (A, B, C) defined by three boolean variables A, B, and C wh...
Explanation:
In the given question, the function F is defined by three boolean variables A, B, and C. The function is expressed as the sum of products, which means it is represented as a logical expression using the AND operator (.) and the OR operator (+).
The given expression is: F = A.B.C A.B.C A.B.C
To convert this expression into the product of sums (POS) form, we need to use the De Morgan's theorem and distribute the negation (complement) over the terms.
The De Morgan's theorem states that the complement of the product of terms is equal to the sum of the complements of the individual terms.
Conversion steps:
1. Apply De Morgan's theorem to the given expression to distribute the negation over the terms.
F = (A + B + C) . (A + B + C) . (A + B + C)
2. Simplify the expression by removing the redundant terms.
F = (A + B + C) . (A + B + C)
3. Apply the distributive property to expand the expression.
F = A.A + A.B + A.C + B.A + B.B + B.C + C.A + C.B + C.C
4. Simplify the expression by removing the redundant terms.
F = A + B + C
Therefore, the product of sums (POS) form of the function F is F = (A + B + C).
Answer:
The correct answer is option 'C': F = (A + B + C) . (A + B + C) . (A + B + C)
In the given question, the function F is defined by three boolean variables A, B, and C. The function is expressed as the sum of products, which means it is represented as a logical expression using the AND operator (.) and the OR operator (+).
The given expression is: F = A.B.C A.B.C A.B.C
To convert this expression into the product of sums (POS) form, we need to use the De Morgan's theorem and distribute the negation (complement) over the terms.
The De Morgan's theorem states that the complement of the product of terms is equal to the sum of the complements of the individual terms.
Conversion steps:
1. Apply De Morgan's theorem to the given expression to distribute the negation over the terms.
F = (A + B + C) . (A + B + C) . (A + B + C)
2. Simplify the expression by removing the redundant terms.
F = (A + B + C) . (A + B + C)
3. Apply the distributive property to expand the expression.
F = A.A + A.B + A.C + B.A + B.B + B.C + C.A + C.B + C.C
4. Simplify the expression by removing the redundant terms.
F = A + B + C
Therefore, the product of sums (POS) form of the function F is F = (A + B + C).
Answer:
The correct answer is option 'C': F = (A + B + C) . (A + B + C) . (A + B + C)
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Community Answer
A function (A, B, C) defined by three boolean variables A, B, and C wh...
F = A̅.B̅.C̅ + A̅.B.C̅ + A.B̅.C̅
In terms of minterms, this can be represented as:
F = ∑m (0, 2, 4)
The equivalent maxterm will contain the terms not present in the minterm representation, i.e.
F = ∑m (0, 2, 4) = π(1, 3, 5, 6, 7) = M1. M3. M5. M6. M7
⇒ (A + B + C̅) (A + B̅ + C̅) (A̅ + B + C̅) (A̅ + B̅ + C) (A̅ + B̅ + C̅)
In terms of minterms, this can be represented as:
F = ∑m (0, 2, 4)
The equivalent maxterm will contain the terms not present in the minterm representation, i.e.
F = ∑m (0, 2, 4) = π(1, 3, 5, 6, 7) = M1. M3. M5. M6. M7
⇒ (A + B + C̅) (A + B̅ + C̅) (A̅ + B + C̅) (A̅ + B̅ + C) (A̅ + B̅ + C̅)
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A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer?
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A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer?.
A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer?.
Solutions for A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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Here you can find the meaning of A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:F = A.B.C + A.B.C + A.B.Cwhere, A, B, and C are the complements of the respective variables. The product of sums (POS) form of the function F isa)F = (A + B + C) . (A + B + C) . (A + B + C)b)F = (A + B + C) . (A + B + C) + (A + B + C)c)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)d)F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
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