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Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B̅, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).
- a)NAND logic can be implemented
- b)OR logic cannot be implemented
- c)NOR logic can be implemented
- d)AND logic cannot be implemented
Correct answer is option 'A,C'. Can you explain this answer?
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Most Upvoted Answer
Consider a Boolean gate (D) where the output Y is related to the input...
A and B can take on two possible values each: 0 (False) or 1 (True).
When A=0 and B=0, Y=0 OR 0 = 0.
When A=0 and B=1, Y=0 OR 1 = 1.
When A=1 and B=0, Y=1 OR 0 = 1.
When A=1 and B=1, Y=1 OR 1 = 1.
Therefore, the output Y is always 1 (True) except when both inputs A and B are 0 (False).
When A=0 and B=0, Y=0 OR 0 = 0.
When A=0 and B=1, Y=0 OR 1 = 1.
When A=1 and B=0, Y=1 OR 0 = 1.
When A=1 and B=1, Y=1 OR 1 = 1.
Therefore, the output Y is always 1 (True) except when both inputs A and B are 0 (False).
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Community Answer
Consider a Boolean gate (D) where the output Y is related to the input...
The given function is,
y = A + B' = (A'B)'
f(A,B) = A+B'
As 0 and 1 are available.
f(0,B) = A + B' = B'= NOT Gate.
f(A,B') = A + (B')' = A + B = OR Gate.
f(o,f(A,B')) = 0 +(A + B)' = NOR Gate.
f(A',B) = A' + B' = (A.B)' = NAND Gate.
f(0,f(A',B)) = 0+((A.B)')' = A.B = AND Gate.
With the combination of OR and NOT, NOR gate can be implemented. Since NOR gate is universal logic gate, so all the functions can be implemented.
Hence, we can implement NOT Gate we can also implement OR, AND, NOR and NAND Gate.
Hence the correct answer is option 1 and option 3.
y = A + B' = (A'B)'
f(A,B) = A+B'
As 0 and 1 are available.
f(0,B) = A + B' = B'= NOT Gate.
f(A,B') = A + (B')' = A + B = OR Gate.
f(o,f(A,B')) = 0 +(A + B)' = NOR Gate.
f(A',B) = A' + B' = (A.B)' = NAND Gate.
f(0,f(A',B)) = 0+((A.B)')' = A.B = AND Gate.
With the combination of OR and NOT, NOR gate can be implemented. Since NOR gate is universal logic gate, so all the functions can be implemented.
Hence, we can implement NOT Gate we can also implement OR, AND, NOR and NAND Gate.
Hence the correct answer is option 1 and option 3.
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Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. Can you explain this answer?
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Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. 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 Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. Can you explain this answer?.
Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. 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 Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y = A + B, where + denotes logical OR operation. The Boolean inputs ‘0’ and ‘1’ are also available separately. Using instances of only D gates and inputs ‘0’ and ‘1’, __________ (select the correct option(s)).a)NAND logic can be implementedb)OR logic cannot be implementedc)NOR logic can be implementedd)AND logic cannot be implementedCorrect answer is option 'A,C'. Can you explain this answer?.
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