# Question on Karnaugh maps

Given this function F(A,B,C,D) = Product-M(4,8,9,11,12) . D(2,3,6,7,10,14)

I know how to get a simplified SOP expression using K-map. However, I'm not sure about simplifying this function until it is K-map ready.

My attempt: (F(A,B,C,D))' = Sum-m(0,1,2,3,5,6,7,10,13,14,15) + d(0,1,4,5,8,9,11,12,13,15)

There are overlapping minterms. So I don't know how to proceed.

• I'd try draw the map if you can't get an answer. I don't fully understand the terms you use. Feb 8, 2013 at 8:34

I'm assuming that your function is in POS form with D() being the don't-cares: $$F(A,B,C,D) = M_4 \cdot M_8 \cdot M_9 \cdot M_{11} \cdot M_{12} \cdot D(2,3,6,7,10,14)$$ If so, since you already know how to compute the simplified version of SOP functions using K-Maps remember that the POS form is a product of maxterms. A maxterm tells you when a boolean function is zero (it is the dual of a minterm, which tells you when the boolean function is one). Therefore plugin a zero in your K-Map for each maxterm: $$M_i$$ and mark your don't cares as you would normally. The empty cells will then be when your function is one, ore your minterms, and since you already know how to simplify the K-Map using those it should be easy.