What is the product of the maxterm and "dont't care" max term of an output in digital system?

Question

"Use a K-map to simplyfy (all possible cases)"

F(A,B,C,D) = ∏(1,5,6,7,9,11,15)⋅D(5,7,10,12)

Specifically, at outputs 5 and 7, how should I interpret them in the Karnaugh map?

I searched up information about this specific problem yet found nothing

Answer 1

Maxterm 5 can be translated to the expression

!A or B or !C or D

Inverting all inputs yields value 0 for A and !B and C and !D

Similarly, maxterm 7 is expressed as

!A or B or C or D

This results in value 0 for A and !B and !C and !D

Your example is described by the following truth table:

A B C D | P   DC   F
--------+---+----+---
0 0 0 0 | 0 |    | 0
0 0 0 1 | 1 |    | 1
0 0 1 0 | 1 |    | 1
0 0 1 1 | 1 |    | 1
0 1 0 0 | 0 |    | 0
0 1 0 1 | 1 | X  | X
0 1 1 0 | 0 |    | 0
0 1 1 1 | 1 | X  | X
1 0 0 0 | 0 |    | 0    inverse of maxterm 7
1 0 0 1 | 0 |    | 0
1 0 1 0 | 0 | X  | 0    inverse of maxterm 5
1 0 1 1 | 1 |    | 1
1 1 0 0 | 1 | X  | X
1 1 0 1 | 1 |    | 1
1 1 1 0 | 0 |    | 0
1 1 1 1 | 1 |    | 1
--------+---+----+---

A don't care condition turns 1 into X.
0 remains 0, because an AND results in 0 if at least one input is 0.

Depicted as a Karnaugh-Veitch map: