COMPUTER SCIENCE AND ENGINEERING
DIGITAL LOGIC
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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X+Y = X . Y
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X.Y = X + Y
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X.Y = X.Y
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None of the above
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Detailed explanation-1: -Explanation: The DeMorgan’s law states that (AB)’ = A’ + B’ & (A + B)’ = A’ * B’, as per the Dual Property. Explanation: (A’B + CD’)’ = (A’B)’(CD’)’ (By DeMorgan’s Theorem) = (A” + B’)(C’ + D”) (By DeMorgan’s Theorem) = (A + B’)(C’ + D). 9.
Detailed explanation-2: -De Morgan’s Theorem, T12, is a particularly powerful tool in digital design. The theorem explains that the complement of the product of all the terms is equal to the sum of the complement of each term. Likewise, the complement of the sum of all the terms is equal to the product of the complement of each term.
Detailed explanation-3: -The second of DeMorgan’s laws tells us that (∼Q)∧(∼P) ( ∼ Q ) ∧ ( ∼ P ) is also true, hence ∼P and ∼Q are both true as well.
Detailed explanation-4: -DeMorgan’s theorem for three variables: (x + y + z)’ = x’y’z’ and (xyz)’ = x’ + y’ + z’ The distributive law: x + yz = (x + y) (x + z) The distributive law: x(y+z) = xy + xz.