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BooleanAlgebra

# BooleanAlgebra - 10 X XY = X 10D X(X Y = X 11(X Y’)Y = XY...

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University of Florida EEL 3701 Dr. Eric M. Schwartz Dept. of Electrical & Computer Engineering Professor in ECE Page 1/1 Laws and Theorems of 29-Aug-01 5:19 PM Boolean Algebra Operations with 0 and 1: 1. X + 0 = X 1D. X • 1 = X 2. X + 1 = 1 2D. X • 0 = 0 Idempotent laws: 3. X + X = X 3D. X • X = X Involution laws: 4. (X’)’ = X Laws of complementarity: 5. X + X’ = 1 5D. X • X’ = 0 Commutative laws: 6. X +Y = Y + X 6D. XY=YX Associative laws: 7. (X +Y) + Z = X + (Y + Z) = X + Y + Z 7D. (XY)Z = X(YZ) = XYZ Distributive laws: 8. X(Y + Z) =XY + XZ 8D. X + YZ = (X +Y)(X + Z) Simplification theorems: 9. XY + XY’ = X 9D. (X + Y)(X + Y’) = X
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Unformatted text preview: 10. X + XY = X 10D. X(X + Y) = X 11. (X + Y’)Y = XY 11D. XY’ + Y = X + Y DeMorgan’s laws: 12. (X + Y + Z + …)’ = X’Y’Z’ 12D. (XYZ…)’ = X’ + Y’ + Z’ 13. [f(A, B, …, Z, 0, 1, +, •)]’ = f(A’, B’, …, Z’, 1, 0, •, +) Duality: 14. (X + Y + Z + …) D = XYZ… 14D. (XYZ…) D = X + Y + Z + … 15. [f(A, B, …, Z, 0, 1, +, •)] D = f(A, B, …, Z, 1, 0, •, +) Theorems for multiplying out and factoring: 16. (X + Y)(X’ + Z) = XZ + X’Y 16D. XY + X’Z = (X +Z)(X’ +Y) Consensus theorems: 17. XY +YZ +X’Z = XY +X’Z 17D. (X + Y)(Y + Z)(X’ + Z) = (X + Y)(X’ +Z)...
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