Given F(A, B,C, D,E) = ∏M (0,3,6,9,11,19,20,24,25,26,27,28,20 ,30) . ∏D (1,2,12,13). Find two minimum SOP expansions for F. Underline the essential prime implicants in your answer.

F = ∑m(4,5,7,8,10,14,15,16,17,18,21,22,23,29,31) ∑m(1,2,12,13)

F = + +

Explanation:

Given data:

F(A,B,C,D,E) = π M (0,3,6,9,11,19,20,24,25,26,27,28,30) π D ( 1,2,12,13 )

The terms given here are maximum so it is called as max terms.

F = ∑m(4,5,7,8,10,14,15,16,17,18,21,22,23,29,31) ∑m(1,2,12,13)

The terms given here are minimum so it is called as min terms.

n = variables = 5

Size of K- map =

Size of K- map =

Size of K- map = 32

For A = 0

The table attached below for A=0, from the sequence of table is calculated.

=

For A = 1

The table attached below for A=1, from the sequence of table is calculated.

From the sequence of table is calculated.

=

The final expression are calculated.

F = + +

F = + +

explanation:

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explanation: