hw5_soln

# hw5_soln - Homework 5 Solutions ECE 0132 1 Problem 1(Brown...

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Homework 5 Solutions ECE 0132 October 13, 2005 1 f ( x 1 , x 2 , x 3 , x 4 ) = Y M (0 , 1 , 2 , 4 , 5 , 7 , 8 , 9 , 10 , 12 , 14 , 15) (1) Figure 1: Karnaugh map for Problem 1(POS) POS form: f ( x 1 , x 2 , x 3 , x 4 ) = ( ¯ x 1 + x 4 ) ( x 2 + x 3 ) ( ¯ x 2 + ¯ x 3 + ¯ x 4 ) ( x 2 + x 4 ) ( x 1 + x 3 ) (2) Figure 2: Karnaugh map for Problem 1(SOP) SOP form: f ( x 1 , x 2 , x 3 , x 4 ) = ¯ x 1 x 2 x 3 ¯ x 4 + x 1 x 2 ¯ x 3 x 4 + ¯ x 2 x 3 x 4 (3) 1

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2 Figure 3: Karnaugh map for Problem 2(POS) POS form: f ( x 1 , x 2 , x 3 , x 4 ) = ( ¯ x 2 + x 3 ) ( x 2 + ¯ x 3 + ¯ x 4 ) ( ¯ x 2 + x 4 ) (4) Figure 4: Karnaugh map for Problem 2(SOP) SOP form: f ( x 1 , x 2 , x 3 , x 4 ) = ¯ x 2 ¯ x 3 + ¯ x 2 ¯ x 4 + x 2 x 3 x 4 (5) 2
3 Problem 3 SOP form: f ( x 1 , x 2 , x 3 , x 4 ) = ¯ x 2 ¯ x 3 + ¯ x 2 ¯ x 4 + x 2 x 3 x 4 (6) = ¯ x 2 ¯ x 3 + ¯ x 2 ¯ x 4 + x 2 x 3 x 4 (7) = ¯ x 2 ¯ x 3 · ¯ x 2 ¯ x 4 · x 2 x 3 x 4 (8)

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hw5_soln - Homework 5 Solutions ECE 0132 1 Problem 1(Brown...

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