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3690885346 - Chapter 2 Boolean Expression Simplification...

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CEG 260, Meilin Liu 1 Chapter 2 Boolean Expression Simplification using BooleanAlgebra Meilin Liu Department of Computer Science Wright State University Homepage: http://www.wright.edu Email: [email protected]
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CEG 260, Meilin Liu 2 1. 3. 5. 7. 9. 11. 13. 15. 17. Commutative Associative Distributive DeMorgan’s 2. 4. 6. 8. X . 1 X = X . 0 0 = X . X X = 0 = X . X Boolean Algebra 10. 12. 14. 16. X + Y Y + X = ( X + Y ) Z + X + ( Y Z ) + = X ( Y + Z ) XY XZ + = X + Y X . Y = XY YX = ( XY ) Z X ( YZ ) = X + YZ ( X + Y )( X + Z ) = X . Y X + Y = X + 0 X = + X 1 1 = X + X X = 1 = X + X X = X
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CEG 260, Meilin Liu 3 Boolean Expression Simplification by Boolean Algebra DeMorgon’s Theorem f(w,x,y,z) = wx(y’z + yz’) f’(w,x,y,z) = w’ + x’ + (y’z +yz’)’ = w’ + x’ + (y’z)’(yz’)’ = w’ + x’ + (y + z’)(y’ + z) = w’ + x’ + yy’ + yz + z’y’ + z’z = w’ + x’ + 0 + yz + z’y’ + 0 = w’ + x’ + yz + y’z’
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CEG 260, Meilin Liu 4 Boolean Expression Simplification by Boolean Algebra DeMorgon’s Theorem F1={(a’+d)’*(a’+c’)’}’ Method 1: F1={(a’+d)’*(a’+c’)’}’={(a’+d)’}’+(a’+c’)’’ =a’+d+a’+c’=a’+a’+d+c’=a’+c’+d Method 2: F1={(a’+d)’*(a’+c’)’}’={(a’’*d’)*(a’’*c’’)}’=(ad’ac)’ =(acd’)’=a’+c’+d
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  • Spring '08
  • Staff
  • Boolean Algebra, Elementary algebra, Algebraic structure, Symmetric difference, Boolean Expression Simplification, Meilin Liu

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