SP10-pp1 - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT OF...

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UC Davis 1 Hussain Al-Asaad U NIVERSITY OF C ALIFORNIA —D AVIS D EPARTMENT OF E LECTRICAL & C OMPUTER E NGINEERING EEC180A — D IGITAL S YSTEMS I Spring 20 10 P RACTICE P ROBLEMS — S ET 1 1. Draw the schematic for the function . 2. Draw the schematic for the following functions using NAND gates and inverters only: a. b. 3. Prove the following simplification theorems using the first eight laws of boolean algebra: a. b. 4. Use DeMorgan’s theorem to compute the complement of the functions: a. b. 5. Using Boolean algebra, verify that the schematic below implements the XOR function. 6. Simplify the function using the theorems of boolean alge- bra. Write the particular law or theorem you are using in each step. For each simplified function, give the number of literals. 7. Given the following function in product of sums form (not necessarily minimized) . a. Express F in the canonical sum of products form using “little m” notation. b. Reexpress F in a minimized sum of products form. c. Express F in minimized sum of products. d. Reexpress F in minimized product of sums. WX YZ + () XYZ [] XY YZ + + + X = + XZ + + = AB CD + Z + X Y F A B C FXY , + + = FWXYZ ,,, WXY ++ WZ + WY + =
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UC Davis 2 Hussain Al-Asaad 8. Use the Karnaugh map to simplify the following functions in the sum of products form.
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SP10-pp1 - UNIVERSITY OF CALIFORNIADAVIS DEPARTMENT OF...

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