Express the complement of the following function in sum of min-terms.

F(A, B, C, D) = Σ(0, 2, 6, 11, 13, 14)

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First of all table of representation:

SN A B C D Min-terms
0 0 0 0 0 A’B’C’D’
1 0 0 0 1 A’B’C’D
2 0 0 1 0 A’BCD’
3 0 0 1 1 A’B’CD
4 0 1 0 0 A’BC’D’
5 0 1 0 1 A’BC’D
6 0 1 1 0 A’BCD’
7 0 1 1 1 A’BCD
8 1 0 0 0 AB’C’D’
9 1 0 0 1 AB’C’D
10 1 0 1 0 AB’CD’
11 1 0 1 1 AB’CD
12 1 1 0 0 ABC’D’
13 1 1 0 1 ABC’D
14 1 1 1 0 ABCD’
15 1 1 1 1 ABCD

Now, complement of following function is

F'(A, B, C, D) = Σ(1, 3, 4, 5, 7, 8, 9, 10, 12, 15)

So, sum of min-terms is

= A’B’C’D + A’B’CD + A’BC’D’ + A’BC’D + A’BCD + AB’C’D’ + AB’C’D + AB’CD’ + AB’CD’ + ABC’D’ + ABCD

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