The Boolean expression provided is:

$Y = f(A, B, C, D) = \Sigma m(1, 3, 7, 8, 10, 12, 13, 15)$

This is a sum of minterms representation, where the given minterms correspond to specific binary combinations of the variables $A$, $B$, $C$, and $D$.

Step 1: Generate the Karnaugh Map (K-Map)

We can simplify this Boolean function by placing these minterms into a 4-variable K-map and applying grouping to simplify the expression.

The binary representations of the minterms are:

• m(1) = 0001
• m(3) = 0011
• m(7) = 0111
• m(8) = 1000
• m(10) = 1010
• m(12) = 1100
• m(13) = 1101
• m(15) = 1111

We will now populate the K-map.

Step 2: Simplification Using the K-Map

From the K-map, we can group adjacent 1's:

• Group 1 (4 cells): m(12), m(13), m(15), m(7) → $C$
• Group 2 (2 cells): m(8), m(12) → $A \overline{B}$
• Group 3 (2 cells): m(3), m(7)