Simplification of function $F(A,B,C,D) = \sum\left(0,2,4,5,8,9,10,12,13\right)$ using Karnaugh Map.

Question

I have been given the function $F(A,B,C,D) = \displaystyle \sum\left(0,2,4,5,8,9,10,12,13\right)$, to simplify using K-Map. I drew the K map shown below: \begin{array}{|c|c|c|c|c|}\hline \large AB\backslash CD\normalsize &00 &01 &11 &10 \\\hline 00 &1 &0 &0 &1 \\ 01 &1 &1 &0 &0 \\ 11 &1 &1 &0 &0 \\ 10 &1 &1 &0 &1 \\\hline \end{array} I grouped the elements as $$\text{quad 1} = m_0 + m_2 + m_8 + m_{10}$$ $$\text{quad 2} = m_4 + m_5 + m_{12} + m_{13}$$ $$\text{quad 3} = m_8 + m_9 + m_{12} + m_{13}$$ In total I formed 3 quads, however my tutor on discussing the solution told that the correct grouping is not including the above mentioned quad 1 and forming a separate quad and pair instead which is : $$\text{quad new} = m_0 + m_4 + m_{12} + m_{8}$$ $$\text{pair 1 } = m_2 + m_{10}$$ The reason he gave was that the new grouping forms more no. of groups(4) than the previous grouping(3)and hence it will be the correct grouping. However I am not convinced as the rule says that we have to form the largest possible group, which here is the quad 1 instead of pair 1. I would really apreciate any help here and some light on the "true rule".

Answer 1

The minimal components (maximal covering, minimal number of letters) in your Karnaugh map are