Question

Express the following function as sum of minterms and product of
maxterms.
F(A,B,C,D) = B’D + A’D + BD

Answer 1

The Sum of minterms and the product of maxterms for the equation is,

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

Given:

F(A, B, C, D)

To Find:

The sum of minterms and product of maxterms = ?.

Solution:

According to the problem, expanding the equation,

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

now, multiply all of it,

= A'(B'+C)+B(B'+C)(C'+D)

= (A'B'+A'C+BB'+BC)(C'+D)

= C'(A'B'+A'C+BB'+BC)+D(A'B'+A'C+BB'+BC)

= A'B'C'+A'CC'+BB'C'+BCC'+A'B'D+A'CD+BB'D+BCD

now, since A', B', and C' are zero, therefore,

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

The Sum of minterms and the product of maxterms for the equation is,

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