Simplify the following Boolean function using K-map Y =∑m(0,1,3,5,6,7,9,11,16,18,19,20,21,22,24,26)

To simplify the given Boolean function using K-map, we first need to create a Karnaugh map (K-map) with the given minterms. The K-map for a 5-variable Boolean function is a 4x4 matrix with two of the variables representing the rows and two representing the columns, and the fifth variable is used to split the K-map into two halves.

Here is the K-map for the given function:

A'B' | 00  01  11  10
----------------------
  00 | 1   1   x   x
  01 | 1   1   x   x
----------------------
  11 | x   x   1   1
  10 | x   x   1   1

A'B' | 00  01  11  10
----------------------
  00 | x   x   1   1
  01 | x   x   1   1
----------------------
  11 | x   x   x   x
  10 | x   x   x   x

In the above K-maps, A and B are the variables for the rows, C and D are the variables for the columns, and E is the variable that splits the K-map into two halves. The 'x' represents a don't care condition.

Now, we need to group the 1's in the K-map. The aim is to form the largest possible groups of 1's, and each group must be a power of 2 (i.e., 1, 2, 4, 8, etc.). Also, the groups can overlap.

From the K-map, we can form three groups of four 1's each. The simplified Boolean function is then the OR of the ANDs of the variables for each group. The variables for a group are those that remain constant (either 0 or 1) within the group.

From the first K-map, we have two groups of four 1's each. The variables for the first group are A'B'C'D' and for the second group are A'B'CD. From the second K-map, we have one group of four 1's. The variables for this group are AB'C'D.

So, the simplified Boolean function is:

Y = A'B'C'D' + A'B'CD + AB'C'D

This is the simplified form of the given Boolean function using K-map.