HW2903_2 - ELEG 2903 / CENG 2113: HW#2 (due Tuesday,...

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ELEG 2903 / CENG 2113: HW#2 (due Tuesday, September 23) Each question is worth 1 point, for a total of 17 points. Show your work, and check your answers. 1) Prove the following relationships using Boolean Algebra by manipulating the left side of the equality until it is the same as the right side. State the specific law/identity used at each step. a) xy + xy’ + x’y’ = x + y’ b) xy + yz + x’z = xy + x’z (consensus theorem) c) (x + y)(y + z)(x + z) = xy + yz + xz 2) Construct the truth table for the following function: f(x, y, z) = yz + (x’ + y)(x’ + z’) 3) For the following truth table, write the corresponding SOP canonical formula in algebraic form and minterm form. x y z | f 0 0 0 | 1 0 0 1 | 1 0 1 0 | 0 0 1 1 | 1 1 0 0 | 0 1 0 1 | 1 1 1 0 | 1 1 1 1 | 0 4) For the following truth table, write the corresponding POS canonical formula in algebraic form and maxterm form. w x y z | f 0 0 0 0 | 0 0 0 0 1 | 1 0 0 1 0 | 1 0 0 1 1 | 0 0 1 0 0 | 1 0 1 0 1 | 0 0 1 1 0 | 1 0 1 1 1 |
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HW2903_2 - ELEG 2903 / CENG 2113: HW#2 (due Tuesday,...

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