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# NAU EE 110 - Homework

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EE 110 Spring 2017 CUPT Homework 4 1. (20 pts) The following is a timing diagram showing the inputs € A,B,C to a logic circuit and its output € f (A,B,C). The horizontal axis represents time. Using this information, find the minimized SOP expression for € f (A,B,C) and draw its logic circuit realization. (Hint: Start by converting the timing diagram to a truth table.) 2. Given the following canonical expression € f ( w, x, y,z) = M (1, 3,6,11,15)∏ a. (15 pts) Use a Karnaugh map to find a minimized SOP expression for € f (w, x, y, z). Show that your solution produces the correct truth table. b. (15 pts) Use a Karnaugh map to find a minimized POS expression for € f (w, x, y, z). Show that your solution produces the correct truth table. Draw a separate K-map for parts (a) and (b) – don’t use a single map for both parts (it becomes too hard to read). Clearly show your groupings.3. Given the following canonical expression € f ( r, s,t,u) = M (3,5, 7,8, 9,14,15)⋅ D(2, 4,13)∏ a. (15 pts) Use a Karnaugh map to find a minimized SOP expression for € f (r, s,t,u). Show that your solution produces the correct truth table. b. (15 pts) Use a Karnaugh map to find a minimized POS expression for € f (r, s,t,u). Show that your solution produces the correct truth table. Draw a separate K-map for parts (a) and (b) – don’t use a single map for both parts (it becomes too hard to read). Clearly show your groupings. 4. Given the following expression € f (A,B,C) = (A + B)(A + B + C)(A + C) a. (10 pts) Use a K-map to find the compact (shorthand) form canonical SOP expression for € f (A,B,C). (Hint: do the K-map process in reverse) b. (10 pts) Use the same K-map to find the compact (shorthand) canonical POS expression for € f

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