Required Problem- Comprehensive. 4 (**). Karnaugh Maps are a tool for simplifying Boolean expressions using a matrix. For example: F(X,Y,Z) = X'YZ' X'YZ XY'Z XYZ' 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: The following are the simplification rules: Each group should contain the largest number of 'ones' (1s) and no blank cells. The number of 'ones' in a group must be a power of two. Grouping is carried-on in decreasing order meaning, one must try to group for 8 (octet) first, then for 4 (quad), followed by 2 and lastly for 1 (isolated 'ones'). Grouping is done either horizontally or vertically or in terms of rectangles/squares. Diagonal grouping of 'ones' is not permitted. The same element(s) may repeat in multiple groups only if this increases the size of the group. The elements around the edges of the matrix, including the four