Boole's/Shannon's Expansion Theorem provides a mechanism to decompose a Boolean function. The Theorem says that a...

 

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Boole's/Shannon's Expansion Theorem provides a mechanism to decompose a Boolean function. The Theorem says that a Boolean expression 'f' of n Boolean variables (X1, X2, ... Xn) can be decomposed as f(X1, X2, ... Xn) = (X1 AND f(1, X2, , Xn)) OR (X1' AND f(0, X2, Xn)) Convince yourself that this decomposition is correct. (Nothing to submit for this) a. Can the OR in the above expression be replaced with an XOR? Justify your answer. Boole's/Shannon's Expansion Theorem provides a mechanism to decompose a Boolean function. The Theorem says that a Boolean expression 'f' of n Boolean variables (X1, X2, ... Xn) can be decomposed as f(X1, X2, ... Xn) = (X1 AND f(1, X2, , Xn)) OR (X1' AND f(0, X2, Xn)) Convince yourself that this decomposition is correct. (Nothing to submit for this) a. Can the OR in the above expression be replaced with an XOR? Justify your answer.

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According Fxx by The OR 4 XOR Let to Assume y Proof f x x XN x F 1 X X 7 Shannons Expansion The o... View the full answer