# HW2 - EE 2301 INTRODUCTION TO DIGITAL SYSTEMS DESIGN...

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EE 2301 S 2010 INTRODUCTION TO DIGITAL SYSTEMS DESIGN HOMEWORK #2 (20 pts) Due Feb. 16, 2010 1. Simplify using algebraic manipulations: (a) a’ (b’ + c) + a + bc’ (b) a b + a’ b c’ + bc (c) z (x’ + y) (x’ y + z) (d) w’ x’ (y’ + z) + w x’ (y + z’) (y’ + z) (e) A’C’D’ + AC’ + BCD + A’CD’ + A’BC + AB’C’ 2. (a) Convert the following expression into SOP form by multiplying out: (A + B + C’) (A + B + D) ( A + B + E) ( A + D’ + E) (A’ + C) (b) Convert the following expression into POS form by factoring: AC + A’ B D’ + A’ B E + A’ C’ D E 3. Problem 3.32 4. (a) Algebraically show that NAND is not associative. (b) Algebraically show that z(x y) = zx zy 5. (a) Given two Boolean functions F 1 and F 2 of the same 5 Boolean variables : F 1 = m (1,6,30) and F 2 = m (1,6,7,8,30) Find the minterm expansion for ( F 1 + F 2 )’ (b) Given two Boolean functions F 1 and F 2 of the same 5 Boolean variables : F 1 = M

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HW2 - EE 2301 INTRODUCTION TO DIGITAL SYSTEMS DESIGN...

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