# Logic Circuits for Boolean Expressions

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1. Using Boolean algebra, reduce the following Boolean expression to its simplest form and implement it using your method of choice.

F = A'B'D + ABC' + AB'CD + BC + A'CD + BCD

2. Using a Karnaugh map (K-map), reduce the following Boolean to its simplest form and implement it using SOP (Sum of Products)

F = B'C'D + B'D + ABC + BC'D' +ABD' + A'B'D

3. Using a Karnaugh map (K-map), reduce the following Boolean to its simplest form and implement it using POS (Products of Sum)

F(A, B, C, D) = ∑(0,2,3,5,7,8,9,10,11,13,15)

Show karnaugh map steps and details.

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This posting contains answers to the logic circuits for Boolean expressions.

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1. Using Boolean algebra, reduce the following Boolean expression to its simplest form and implement it using your method of choice.

F = A'B'D + ABC' + AB'CD + BC + A'CD + BCD

Solution: We first group the terms with common logic:

F = A'B'D + B(AC'+C) + CD(AB'+A') + BCD

Then we apply Boolean algebra laws to simplify the highlighted terms:

F = A'B'D + B(A+C) + CD(A+B') + BCD

Then ...

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