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WI12-pp1-sol

# WI12-pp1-sol - UNIVERSITY OF CALIFORNIA-DAVIS 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 Winter 2012 S OLUTIONS OF P RACTICE P ROBLEMS — S ET 1 1. Draw the schematics of in terms of AND, OR, and inverter gates. 2. Draw the schematics of the following functions in terms of NAND and inverter gates. 3. (a) Prove the simplification theorem using the first eight laws of Boolean algebra (page 51 of textbook). There are several answers to this problem. Below is one of them. = Distributive law (8) Distributive law (8) Complementarity theorem (5D) Operations with 0 (1) Idempotent theorem (3D) Commutative law (6D) F W X YZ + = W X Y Z F X Y Z a) X YZ XYZ = X Y Z b) XY XZ + XY XZ + XY XZ = = X Y + X Y + X = X Y + X Y + X X Y + Y X Y + + XX XY YX YY + + + XX XY YX 0 + + + XX XY YX + + X XY YX + + X XY XY + +

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