K-Map
K-map is basically a box of several squares adjacent to each other. The number of squares in a box depends upon the number of variables used in
that function. This relation is:

Normally K-maps are created for 2 or 3 or 4 variable functions. However it can be created for functions having even large number of variables as
well. Here is how these maps look like:

Simplification Process-

Prepare the respective map depending upon the number of variables used in the function.

Put 1 on appropriate places for every min-term provided in the function.

Make groups of 1’s in the map. Although Karnaugh has introduced several rules for grouping. These are:

groups can be made in exponents of 2 only.

Only adjacent squares can be grouped. Diagonal grouping is not allowed.

Always try to make the largest possible group.

Gaps are not allowed in between groups.

Min-terms that reside on boundaries of map can undergo external adjacency and hence can be grouped along.

Unnecessary grouping should be avoided.

If any min-term is left ungrouped, it should be evaluated solely.

Rules for deploying K-map in finding SOP Expression:

For evaluation of min-terms, following rules are to be used:

If complete group falls under normal variable, it will be written normally.

If complete group falls outside of normal variable, it will be written inversely.

If half of the group falls under any variable, it will not be considered.