BooleanAlgebra - Consensus theorem XY YZ X'Z = XY X'Z(X Y(Y...

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LAWS AND THEOREMS OF BOOLEAN ALGEBRA Distributive laws: X(Y + Z) = XY + XZ X + YZ = (X + Y)(X + Z) Simplification theorems: XY + XY' = X (X + Y)(X + Y') = X X + XY = X X(X + Y) = X (X + Y')Y = XY XY' + Y = X + Y Multiplying out and Factoring: (X + Y)(X' + Z) = XZ + X'Y XY + X'Z = (X + Z)(X' + Y)
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Unformatted text preview: Consensus theorem: XY + YZ + X'Z = XY + X'Z (X + Y)(Y + Z)(X' + Z) = (X + Y)(X' + Z) Exclusive Or and Equivalence: X ⊕ Y = X'Y + XY' X ≡ Y = XY + X'Y' Tom Penick [email protected] www.teicontrols.com/notes December 8, 1997...
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