Simplify the following expressions to the simplest expression using De Morgan's theorem and Boolean algebra.
ABC+A'CD+B'CD
=(AB+A'D+B'D)C
=(AB+(A'+B')D)C
=(AB+(AB)'D)C
can anyone simplify it further and explain how you got there.Thanks in advance.
2026-03-28 19:30:10.1774726210
Simplification of the boolean expression using boolean algebra
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It always helps to expand the terms so they include all variables .. and then reorganize, and recombine in a more efficient way, adding or removing duplicates as needed.
The key principle is:
Adjacency
$P = PQ + PQ'$
Starting from your second expression:
$(AB+A'D+B'D)C=$
$(ABD+ABD'+A'BD+A'B'D+AB'D+A'B'D)C=$
$(ABD+ABD'+(AB+A'B+AB'+A'B')D)C=$
$(AB+(B+B')D)C=$
$(AB+D)C$