Question

Use a K-Map to find a minimum sum of products (SOP) expression for the following function

F(A,B,C,D) = (A' + B' + C)(A + C + D') + ABC'D

Answer 1

To find a minimum SOP expression for the function F(A,B,C,D) using a K-Map, you need to create a K-Map, fill it according to the function, group the '1's, and derive the simplified sum of product terms.

Step-by-step explanation:

The student's question involves finding a minimum sum of products (SOP) expression using a Karnaugh map (K-Map). The question given is F(A,B,C,D) = (A' + B' + C)(A + C + D') + ABC'D. To simplify the function using a Karnaugh map, follow these steps:

1. Create a K-Map for a four-variable function.
2. Transfer the given function into the K-Map, placing a '1' where the function is true and a '0' where the function is false.
3. Group adjacent '1's together in powers of two (i.e., 1, 2, 4, 8...).
4. From these groups, generate a sum of product terms that represents the grouped ones.
5. Combine the terms, if possible, to minimize the number of literals in each term.

This method aims to reduce the original function into a simpler form by eliminating redundant terms or combining terms using the properties of Boolean algebra. As a result, the student will end up with a minimal SOP expression for the given function.