Map Simplification:-

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-
  1. Prepare the respective map depending upon the number of variables used in the function.
  2. Put 1 on appropriate places for every min-term provided in the function.
  3. 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:
  1. 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.