Which K-map to chose?

Question

I got a K-map with the following boolean function: F(A,B,C,D) = ΠM[3,4,6,9,11,14]+ Σm[0,7,8,10,13,15]

In the following K-map following prime-implicants are considered:

But I can chose ($\bar{A}$+$\bar{D}$) instead of ($\bar{A}$+$B$) like:

So now I get f = ($\bar{A}$+$\bar{D}$)($\bar{B}$+$\bar{C}$)($\bar{C}$+$\bar{D}$)($A$+$C$+$D$)

So we get different f in the two cases or am I making a mistake somewhere? Please correct me where I'm doing it wrong

Answer 1

Your two solutions are correct. I checked them with Logic Friday 1. Depending on your choice how to merge blocks in the Karnaugh-Veitch map, you are arriving at different alternative solutions.

(!c+!d) & (!b+!c) & (!a+!d) & (a+!b+d)


!b!d + a!c!d + !a!cd

             cd
       00  01  11  10
      +---+---+---+---+
   00 | 1 | 1 | 0 | 1 |
      +---+---+---+---+
   01 | 0 | 1 | 0 | 0 |
ab    +---+---+---+---+
   11 | 1 | 0 | 0 | 0 |
      +---+---+---+---+
   10 | 1 | 0 | 0 | 1 |
      +---+---+---+---+

You might be interested in this Karnaugh-Veitch online tool to verify your results.

Answer 2

Both approaches are correct, both are correct solutions:

($\bar{A}$+$\bar{D}$)($\bar{B}$+$\bar{C}$)($\bar{C}$+$\bar{D}$)($A$+$C$+$D$)

($\bar{A}$+$B$)($\bar{B}$+$\bar{C}$)($\bar{C}$+$\bar{D}$)($A$+$C$+$D$)