# Logic Circuits for Boolean Expressions

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) = âˆ‘(0,2,3,5,7,8,9,10,11,13,15)

Show karnaugh map steps and details.

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#### Solution Preview

Please see attached for the full solution to the given problems.

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 ...

#### Solution Summary

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