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Math Forum / Mathematics / Algebra Help / July 2009Boolean algebra help
Can anyone help simplify? ( A * B * C * D ) + ( A * B * E * C') > Can anyone help simplify? > > ( A * B * C * D ) + ( A * B * E * C') abcd + abec' = ab(cd + ec') disjunctive normal form = ab(cd + e)(cd + c') = ab(c + e)(d + e)(c + c')(d + c') = ab(c + e)(d + e)(d + c') conjunctive normal form = ab(cd + e)(d + c') = ab(cd + ed + ec') = ab(cd + edc + edc' + ec') = ab(cd + ec') = abcd + abec' The simplified choice is yours. In article <c73df9ff-4938-41d9-8e7d-b019f1b9b4d8@d32g2000yqh.googlegroups.com>, > Can anyone help simplify? > > ( A * B * C * D ) + ( A * B * E * C') What form is considered "simple"? Really, that's a serious question. Your expression is already in DNF (Disjunctive Normal Form), which is considered the simplest form in some contexts. In other contexts, CNF (Conjunctive Normal Form) is considered the simplest. In still other contexts, the factoring with the fewest total terms is considered the simplest. So, as stated, without any additional context, this is an ill-formed problem.  Signature--------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum viditur. | BBB aa a r bbb | ----------------------------- I guess I was thinking that the C and C' on opposite sides of the plus- sign could be combined with a common multiple. I'll go with the disjuntive normal form. Thanks |
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