Discussion Solutions 3

Discussion Solutions 3 - Discussion Solution 3: 1. Multiply...

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Discussion Solution 3: 1. Multiply out to obtain a sum of products: (Simplify where possible.) (W+X' + Z') (W' + Y') (W' +X+Z')(W+X')(W+Y+Z) (W+X'+Z’) (W'+Y’)(W'+X+Z’) (W+X’) (W+Y+Z) = (W+X’) ( W’ +Y’)( W' +X+Z’)(W+Y+Z) = (W+X’) [W’+Y’(X+Z’)] (W+Y+Z) = ( W +X’(Y+Z))[ W ’+Y’(X+Z)] = WY’(X+Z’)+W’X’(Y+Z) = WY’X+ WY’Z’+W’X’Y+ W’X’Z 2. Factor to obtain a product-of-sums: (Simplify where possible.) BCD + C'D' + B'C'D + CD BCD + C’D’ +B’C’D + CD = C D + C’ (D’ + B’D) = (C’+ D) [C + (D’+ B’D)] = (C’ + D) [C + (D’+ B) (D’+D)] = (C’+ D) (C+D'+B) 3. Write an expression for F and simplify the following circuit F = AB [(A D) +D] = AB (AD+A’D’+ D) = AB (A’D’+D) = AB (A’+D) = (AB)’(A’+D) +AB(A’+D)’ = (A’+ B’) (A’+ D) +AB(AD’) = A’+B’D+ABD’ = A’+A BD’+B’D = A’+BD’+B’D
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4. Simplify A’C’D’+AC’+BCD+A’CD’+A’BC+AB’C’ BC A BCD C A D A BC
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Discussion Solutions 3 - Discussion Solution 3: 1. Multiply...

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