# Which K-map to chose?

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

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.

Both approaches are correct, both are correct solutions:

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

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