F(X, Y, Z, W) = π(0, 1, 2, 3, 4, 6, 8, 9, 11, 12) Reduce the Boolean function F(X, Y, Z, W) = π(0, 1, 2, 3, 4, 6, 8, 9, 11, 12) by using 4-variable…

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Reduce the following using a Karnaugh map.

F(X, Y, Z, W) = π(0, 1, 2, 3, 4, 6, 8, 9, 11, 12) Reduce the Boolean function F(X, Y, Z, W) = π(0…

$F(X, Y, Z, W) = \pi(0, 1, 2, 3, 4, 6, 8, 9, 11, 12)$

(a)[4]

Reduce the Boolean function $F(X, Y, Z, W) = \pi(0, 1, 2, 3, 4, 6, 8, 9, 11, 12)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

(b)[1]

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Draw: logic gate diagram for the reduced expression

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Answer

Answer (a)

Groups: (0, 2, 4, 6) → (X + W); (1, 3, 9, 11) → (Y + W'); (0, 4, 8, 12) → (Z + W)

Reduced expression: F = (X + W)(Y + W')(Z + W)

Quad (0, 2, 4, 6) gives (X + W). Quad (1, 3, 9, 11) gives (Y + W'). Quad (0, 4, 8, 12) gives (Z + W). There is no octet.

Answer (b)

Logic gate diagram for $F = (X + W)(Y + W')(Z + W)$: three 2-input OR gates feeding one 3-input AND gate.