There are the following steps to find the minterm solution or K-map:

Step1: First, we define the given exp in canonical form:

Step2: Next, we create k-map by entering 1 to each product term into the k-map cell and fill the remaining cells with zeros.

Step3: Next, we form the groups by considering each one in the k-map. Notice that each group should have largest number of “1”’s.

Step4: We group the number of ones in the decreasing order. First, we have to try to make the group of eight, then for four, after that two and lastly for 1.

Step5: In horizontally or vertically manner, the groups of ones are formed in shape of rectangle and square. We cannot perform the diagonal grouping in K-map.

Step6: The elements in one group can also be used in different groups only when the size of the group is increased.

Step7: The elements located at the edges of the table are considered to be adjacent. So, we can group these elements.

Step8: We can consider the ‘don’t care condition’ only when they aid in increasing the group-size. Otherwise, ‘don’t care’ elements are discarded.

Step9: In the next step, we find the boolean expression for each group. By looking at the common variables in cell-labeling, we define the groups in terms of input variables. In the below example, there is a total of two groups, i.e., group 1 and group 2, with two and one number of ‘ones’.

In the first group, the ones are present in the row for which the value of A is 0. Thus, they contain the complement of variable A. Remaining two ‘ones’ are present in adjacent columns. In these columns, only B term in common is the product term corresponding to the group as A’B. Just like group 1, in group 2, the one’s are present in a row for which the value of A is 1. So, the corresponding variables of this column are B’C’. The overall product term of this group is AB’C’.

Example1: Y=A’B’ + A’B+AB

Simplified expression:

Example2: A’B’C’+A’ BC’+AB’ C’+AB’ C+ABC’+ABC

Simplified expression:

Example3: Y=A’B’C’ D’+A’ B’ CD’+A’ BCD’+A’ BCD+AB’ C’ D’+ABCD’+ABCD

Simplified expression: