GATE Exam > GATE Questions > Let the two boolean functions as shown below...
Start Learning for Free
Let the two boolean functions as shown below -
F = AB'C + AB + A' + B' + C'
G = A'BC' + A'B + A'B' + B'
Which of the following is true regarding the above functions?
- a)Function {F} is functionally complete.
- b)Function {G} is functionally complete.
- c)Function {F} and {G} both are functionally complete
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Let the two boolean functions as shown below -F = AB'C + AB + A' + B'...
F = AB'C + AB + A' + B' + C'
= A[B'C+B] + A' + B' + C'
= A[B+C] +A' + B' + C' {DISTRIBUTIVE PROPERTY}
= A' + B + C + B' + C'
= T
Now, for function G-
G = A'BC' + A'B + A'B' + B'
= A'[BC' + B + B'] + B'
= A'[BC' + 1] + B'
= A' + B'
= (A.B)'
Which is a NAND gate so the function {G} is functionally complete.
Most Upvoted Answer
Let the two boolean functions as shown below -F = AB'C + AB + A' + B'...
To determine whether the given boolean functions are functionally complete or not, we need to check if they can express all possible boolean functions. In other words, we need to verify if we can use the given functions to construct any desired boolean function.
Let's analyze each function separately:
Function F = AB'C + AB + A' + B' + C'
- F has 5 terms: AB'C, AB, A', B', and C'. Each term represents a combination of inputs that results in a true output.
- F includes all possible combinations of the inputs A, B, and C.
- However, F does not include any negation operation (not operator).
- Since F does not include negation, it cannot express all possible boolean functions.
- Therefore, option (a) can be eliminated.
Function G = A'BC' + A'B + A'B' + B'
- G has 4 terms: A'BC', A'B, A'B', and B'. Each term represents a combination of inputs that results in a true output.
- G includes all possible combinations of the inputs A and B, and their negations.
- G also includes the negation of input C.
- Since G includes negation operations, it can express all possible boolean functions.
- Therefore, option (b) is correct.
Conclusion:
- Function G is functionally complete as it can express all possible boolean functions.
- Function F is not functionally complete as it cannot express all possible boolean functions.
- Hence, option (b) is the correct answer.
Let's analyze each function separately:
Function F = AB'C + AB + A' + B' + C'
- F has 5 terms: AB'C, AB, A', B', and C'. Each term represents a combination of inputs that results in a true output.
- F includes all possible combinations of the inputs A, B, and C.
- However, F does not include any negation operation (not operator).
- Since F does not include negation, it cannot express all possible boolean functions.
- Therefore, option (a) can be eliminated.
Function G = A'BC' + A'B + A'B' + B'
- G has 4 terms: A'BC', A'B, A'B', and B'. Each term represents a combination of inputs that results in a true output.
- G includes all possible combinations of the inputs A and B, and their negations.
- G also includes the negation of input C.
- Since G includes negation operations, it can express all possible boolean functions.
- Therefore, option (b) is correct.
Conclusion:
- Function G is functionally complete as it can express all possible boolean functions.
- Function F is not functionally complete as it cannot express all possible boolean functions.
- Hence, option (b) is the correct answer.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
Question Description
Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let the two boolean functions as shown below -F = AB'C + AB + A' + B' + C'G = A'BC' + A'B + A'B' + B'Which of the following is true regarding the above functions?a)Function {F} is functionally complete.b)Function {G} is functionally complete.c)Function {F} and {G} both are functionally completed)None of the aboveCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup