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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?
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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.
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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?
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