Solved: Cover the answers to this exercise with a sheet of

Chapter 5, Problem 5.1

(choose chapter or problem)

Cover the answers to this exercise with a sheet of paper and slide it down as you check your answers. Write your answers in the space provided before looking at the correct answer.

Determine the minimum sum of products and minimum product of sums for

                    \(f=b^{\prime} c^{\prime} d^{\prime}+b c d+a c d^{\prime}+a^{\prime} b^{\prime} c+a^{\prime} b c^{\prime} d\)

First, plot the map for f.

                   

(a) The minterms adjacent to \(m_0\) on the preceding map are _________ and _________.

(b) Find an essential prime implicant containing \(m_0\) and loop it.

(c) The minterms adjacent to \(m_3\) are _________ and _________.

(d) Is there an essential prime implicant which contains \(m_3\)?

(e) Find the remaining essential prime implicant(s) and loop it (them).

Loop the remaining 1’s using a minimum number of loops. The two possible minimum sum-of-products forms for f are

f = ___________________________________ and

f = ___________________________________

Next, we will find the minimum product of sums for f. Start by plotting the map for \(f^\prime\). Loop all essential prime implicants of \(f^\prime\) and indicate which minterm makes each one essential.

                   

Loop the remaining 1’s and write the minimum sum of products for \(f^\prime\).

\(f^\prime\)= __________________________________

The minimum product of sums for f is therefore

f = __________________________________