Question

11. Multiply out POS expressions using the second distributive law to obtain SOP expres sions, eliminate redundant terms (a) (2 Points) (A+BC(A+D)(B+C) (b) (3 Points) (A+BCAD)(BCD+E+F Factor the SOP expressions using the second distributive law to obtain POS expressions, eliminate redundant terms (a) (2 Points) AB'C+ CD (b) (3 Points) AC+B'CD
Please do all four parts

Answer 1

Second distribution law (a) (x + y) middot (x + z) = x + y z (b) x + y z = (x + y) (x + z) rightarrow For the POS expression, we are using second distributive law as (x + y) middot (x + z) = x + y middot z (a) (A + BC) (A + D) (B' + C') Using second distributive law in first two terms => (A + BCD) middot (B' + C') => (A + BCD) middot (B' + C' + A - A) => (A + BCD) middot (A + (B' + C' - A)) Again using second distributive law => A + BCD middot (B' + C' - A) Using first distributive law => A + BCD middot B' + BCD middot C' - BCDA => A + (B middot B') CD + B (C middot C') middot D - ABCD (using commutative law)
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