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

Chapter 6, Problem 6.1

(choose chapter or problem)

Cover the answers to this exercise with a sheet of paper and slide it down as you check your answers.

Find a minimum sum-of-products expression for the following function:

                    \(f(A, B, C, D, E) = \Sigma m(0, 2, 3, 5, 7, 9, 11, 13, 14, 16, 18, 24, 26, 28, 30) \)

Translate each decimal minterm into binary and sort the binary terms into groups according to the number of 1’s in each term.

Compare pairs of terms in adjacent groups and combine terms where possible. (Check off terms which have been combined.)

Now, compare pairs of terms in adjacent groups in the second column and combine terms where possible. (Check off terms which have been combined.) Check your work by noting that each new term can be formed in two ways. (Cross out duplicate terms.)

Can any pair of terms in the third column be combined? Complete the given prime implicant chart.

Determine the essential prime implicants, and cross out the corresponding rows and columns.

Note that all remaining columns contain two or more X’s. Choose the first column which has two X’s and then select the prime implicant which covers the first X in that column. Then, choose a minimum number of prime implicants which cover the remaining columns in the chart.

From this chart, write down the chosen prime implicants in 0, 1, and – notation. Then, write the minimum sum of products in algebraic form.

The prime implicant chart with the essential prime implicants crossed out is repeated here. Find a second minimum sum-of-products solution.