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Boolean Algebra and Logic Simplification

Q1:

Use Boolean algebra to find the most simplified SOP expression for F = ABD + CD + ACD + ABC + ABCD.

A F = ABD + ABC + CD

B F = CD + AD

C F = BC + AB

D F = AC + AD

ANS:A - F = ABD + ABC + CD

ABD + CD + ACD + ABC + ABCD.
= CD + ACD + ABD + ABC(D+D') + ABCD,
= CD(1+A) + ABD + ABCD + ABCD'+ ABCD,
= CD + ABD(1+C) + ABC(D'+D) {1+C=1, D+D'=1}.
= CD + ABD + ABC.



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