Reduce the Boolean function F(A,B,C,D) = π (0,1,2,3,7,8,9,10,11,12,13,15) by using 4-variable…

Reduce the Boolean function $F(A,B,C,D) = \pi (0,1,2,3,7,8,9,10,11,12,13,15)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

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Answer

Groups: (0, 1, 2, 3, 8, 9, 10, 11) → B; (8, 9, 12, 13) → (A' + C); (3, 7, 11, 15) → (C' + D')

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

Octet (0, 1, 2, 3, 8, 9, 10, 11) gives B. Quad (8, 9, 12, 13) gives (A' + C). Quad (3, 7, 11, 15) gives (C' + D').