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04s_cpe422_hw1_solution_p1

# 04s_cpe422_hw1_solution_p1 - The University of Alabama in...

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The University of Alabama in Huntsville Electrical & Computer Engineering CPE/EE 422/522 Spring 2004 Homework #1 Solution 1. (20 points) Prove the identity of each of the following Boolean equations using algebraic manipulation. a. XY XY XY X Y + + = + XY XY XY XY XY XY XY X Y Y Y X X X Y + + = + + + = + + + = + ( ) ( ) b. XY XY XY XY + + + = 1 XY XY XY XY XY XY XY XY Y X X C X X Y Y + + + = + + + = + + + = + = ( ) ( ) 1 c. X XY XZ XYZ X Y Z + + + = + + X XY XZ XYZ X XY XZ Y X X X Y XZ X XZ Y X X X Z Y X Z Y + + + = + + + = + + + = + + = + + + = + + ( ) ( )( ) ( )( ) 1 d. XY YZ XZ XY XZ + + = + XY YZ XZ XY YZ X X XZ XY XYZ XYZ XZ XY Z XZ Y XY XZ + + = + + + = + + + = + + + = + ( ) ( ) ( ) 1 1 (15 points) Obtain the truth table of the following functions and express each function in sum of minterms and product of maxterms. a. (XY + Z)(Y + XZ) = Σ m (3, 5, 6, 7)= Π M (0, 1, 2, 4) X Y Z XY+Z Y+XZ F 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 b. ( )( ) A B B C + + = Σ m (0, 1, 3, 5, 7)= Π M (2, 4, 6) A B C A’+B B’+C F 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 c. YZ WXY WXZ W XZ + + + = Σ m (1, 3, 5, 9, 12, 13, 14) =

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04s_cpe422_hw1_solution_p1 - The University of Alabama in...

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