Electrical – K-maps, do they completely simplify

boolean-algebrakarnaugh mapstate-machines

I've been told that K-maps produce a completely simplified boolean equation, and they can't or shouldnt be simplified anymore after that. However, on allaboutcircuits.com they were able to simplify an equation more after the k-map. So what gives? Is this just an exception? Or is there something else I'm missing?

This is the k-map in question.
K-map D.a
As you can see, D.a is simplified further after the k-map is done. It goes from AI + BI to (A+B)*I

For context, here's the full article. https://www.allaboutcircuits.com/textbook/digital/chpt-11/finite-state-machines/

Best Answer

The K-Map is producing either the minimal Sum Of Products (SOP), if "circling" the ones, or the minimal Product of Sums (POS), if circling the zeros. Let's do the latter (my grouping is using the red line):

enter image description here

Now, the group of 4 is giving us \$I\$ (as it is the only term which has the same value of \$0\$ in this group) and the group of two is giving us \$A+B\$. So the final result is \$I\cdot(A+B)\$.