Karnaugh Maps are a tool for simplifying Boolean expressions using a matrix. For example:

F$($X$,$Y$,$Z$)=$ X$\text{'}$YZ$\text{'}+$ X$\text{'}$YZ $+$ XY$\text{'}$Z $+$ XYZ$\text{'}+$ XYZ

Using sigma notation, the expression above can be represented in Sum of Product $($SOP$)$ form as:

F$($X$,$Y$,$Z$)=$ m $(2,3,5,6,7)$

The numbers listed above are the locations where the minterm values in the K Map evaluate to $1($true$).$ The

fill order with the matrices $(2,3$ and $4$ variables$)$ below use Gray code: