Discussion Solutions 2

# Discussion Solutions 2 - = X(W X(W Y(W Z = X(W Y(W Z f A BC...

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Discussion Solutions 2: 2.1 Prove the following theorems algebraically: a. X(X’+Y)=XY XX’+XY=0+XY=XY b. X+XY=X X(1+Y)=X 2.3 Simplify by applying one of the theorems. a. X’Y’Z + (X’Y’Z)’ = A + A’ =1 c. ACF+AC’F = AFC+AFC’=AF e. (A’B+C+D)(A’B+D) = A’B+D 2.5 Multiply out and obtain the sum of products a. (A+B)(C+B)(D’+B)(ACD’+E) = (AC+B)(D’+B)(ACD’+E) (Theo 8) = (ACD’+B)(ACD’+E) (Theo 8) = (ACD’+BE) (Theo 8) 2.6 Obtain a product of sums a. AB+C’D’ = (AB+C’)(AB+D’) = (A+C’)(B+C’)(A+D’)(B+D’) b. WX+WY’X+ZYX = WX+XYZ = (W+XYZ) (X+XYZ) = (W+XYZ) (X) = (W+X)(W+Y)(W+Z)X

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Unformatted text preview: = X (W+X)(W+Y)(W+Z) = X (W+Y)(W+Z) f. A+BC+DE = (A+BD+D)(A+BC+E) = (A+B+D)(A+D+D)(A+B+E)(A+C+E) = (A+B+D)(A+B+E)(A+C+E) 2.8 Simplify the following expressions to a minimum sum of products: a. [(AB)’+C’D]’ = ((AB)’+C’D)’ = ((AB)’)’ . (C’D)’ = AB.(C+D’) = ABC + ABD’ Obtain the sum of products of (A+B’)(A+C+D)(A+B’+D) D B C B A D C B A B A D C A D B A D C A B A + + = + + = + + + = + + + + + ) ( ) )( ( ) )( )( ( X B X A X B A = = = + Obtain the sum of products of (A+B’)(A’+C)(C+D)(B+D) D A BC BC D BC A D B D C C A B A + = + + = + + + + ) )( ( ) )( )( )( ( X BC =...
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