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hw3_soln - Homework 3 Solutions ECE 0132 1 Problem 1 x y F...

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Unformatted text preview: Homework 3 Solutions ECE 0132 September 28, 2005 1 Problem 1 x y F F 1 F 2 F 3 F 4 F 5 F 6 F 7 F 8 F 9 F 10 F 11 F 12 F 13 F 14 F 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.1 (a) A realization for each function: F = 0 (1) F 1 = xy (2) F 2 = x ¯ y (3) F 3 = x ¯ y + xy (4) F 4 = ¯ xy (5) F 5 = ¯ xy + xy (6) F 6 = ¯ xy + x ¯ y (7) F 7 = ¯ xy + x ¯ y + xy (8) F 8 = ¯ x ¯ y (9) F 9 = ¯ x ¯ y + xy (10) F 10 = ¯ x ¯ y + x ¯ y (11) F 11 = ¯ x ¯ y + x ¯ y + xy (12) F 12 = ¯ x ¯ y + ¯ xy (13) F 13 = ¯ x ¯ y + ¯ xy + xy (14) F 14 = ¯ x ¯ y + ¯ xy + x ¯ y (15) F 15 = 1 (16) 1 1.2 (b) To test if a function is commutative, replace x with y and y with x . If the truth table is the same, the function is commutative. F = → (17) F 1 = xy → yx (18) F 2 = x ¯ y → y ¯ x (19) F 3 = x ¯ y + xy → y ¯ x + yx (20) F 4 = ¯ xy → ¯ yx (21) F 5 = ¯ xy + xy → ¯ yx + yx (22) F 6 = ¯ xy + x ¯ y → ¯ yx + y ¯ x (23) F 7 = ¯ xy + x ¯ y + xy → ¯ yx + y ¯...
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hw3_soln - Homework 3 Solutions ECE 0132 1 Problem 1 x y F...

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