Question

Consider the Boolean function F given by

F(A,B,C,D) = ∑(0,2,5,6,10,13,15)
d(A,B,C,D) = ∑7,9,11)
Using four variable K-map, find the simplified sum of products (SoP) and the simplified product of sums (PoS) form of the function F. Please give your answer as a function of A,B,C, and D.

Answer 1

The student's question regarding the four-variable Karnaugh map simplification for the SoP and PoS can be solved by grouping the corresponding terms on the K-map and deriving the simplified Boolean expressions.

Step-by-step explanation:

The student asked about finding the simplified sum of products (SoP) and the simplified product of sums (PoS) for a Boolean function using a four-variable Karnaugh map (K-map). The function is given by F(A,B,C,D) = Σ(0,2,5,6,10,13,15) with a don't care condition d(A,B,C,D) = Σ(7,9,11).

To find the simplified SoP, group the 1s including the don't care terms in the K-map to create the largest possible groups of 2, 4, or 8. Then derive the SoP expression from these groups. For the PoS form, instead group the 0s (excluding the don't care terms), and find the largest possible groups to drive the PoS expression.

After performing the grouping and simplification, you can write down the simplified expressions for SoP and PoS as functions of A, B, C, and D.