Reduce the Boolean function F(A, B, C, D) = π(0, 2, 4, 6, 8, 9, 10, 11, 14) by using 4-variable Karnaugh map, showing the various groups (i.e., octal…

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Reduce the following using a Karnaugh map.

Reduce the Boolean function F(A, B, C, D) = π(0, 2, 4, 6, 8, 9, 10, 11, 14) by using 4-variable…

Reduce the Boolean function $F(A, B, C, D) = \pi(0, 2, 4, 6, 8, 9, 10, 11, 14)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs). Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

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Answer

Groups: (8, 9, 10, 11) → (A' + B); (0, 2, 4, 6) → (A + D); (2, 6, 10, 14) → (C' + D)

Reduced expression: F = (A' + B)(A + D)(C' + D)

Quad (8, 9, 10, 11) gives (A' + B). Quad (0, 2, 4, 6) gives (A + D). Quad (2, 6, 10, 14) gives (C' + D). There is no octet. Logic gate diagram: three 2-input OR gates feeding one 3-input AND gate.