When asking whether a 1 makes a group of four an essential prime
implicant on a four-variable map, we need find only two adjacent 0’s. If
there are fewer than two adjacent 0’s, this 1 must be either in a group of
eight or part of two or more smaller groups. Note that in Example 3.8, m2
and m14 have two adjacent 0’s, and thus each makes a prime implicant
essential. In contrast, m0, m4, m8, and m12 each have only one adjacent 0
and are each covered by two or three prime implicants.
We will now consider some examples with multiple minimum solutions,
starting with the three-variable function used to illustrate the definition
of terminology in Section 2.2.3.