3.a Draw the logic diagram for the following Boolean expression. The diagram should correspond exactly to...

3.a Draw the logic diagram for the following Boolean expression. The diagram should correspond exactly to the equation (do not simplify). Assume that the complements of the inputs are available. ? = ?′?(? + ?) + ??′(? + ?) + ?′?(? + ?) + ??′(? + ?) b. Simplify the Boolean expression in (a) using a Karnaugh Map, then draw the corresponding two-level logic diagram as a sum of products implementation.

Solutions

Expert Solution

3) a) Given Boolean expression

? = ?′?(? + ?) + ??′(? + ?) + ?′?(? + ?) + ??′(? + ?)

Circuit:

Given ? = ?′?(? + ?) + ??′(? + ?) + ?′?(? + ?) + ??′(? + ?)

Above Function in K-map as follows

Simplified K-map as follows

The Simplified SOP of F (W, X, Y, Z) = W’XY+XYZ’+XY’Z+WX’Y +WX’Z

Simplified Circuit: F (W, X, Y, Z) = W’XY+XYZ’+XY’Z+WX’Y +WX’Z

Explanation:
Negation(¬) of any logical Identity P is Nothing but Opposite Truth Value for P. i.e If P is T then (¬P) is F
And gate is used to find the Product of Two literals P AND Gate Q Output is PQ
OR gate is used to find the Sum of Two literals P OR Gate Q Output is P+Q

venereology answered 1 year ago

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