It is sometimes possible to save logic by using more than

Chapter 15, Problem 15.5

(choose chapter or problem)

It is sometimes possible to save logic by using more than the minimum number of flip-flops. For both (a) and (b), fill in each state assignment by columns and, then, check for duplicate rows instead of filling in the assignments by rows and checking for permuted columns. If the columns are assigned in ascending numerical order and the first row is all 0’s, then equivalent assignments will not be generated. Do not list degenerate assignments for which two columns are identical or complements of each other, or assignments where one column is all 0’s or all 1’s.

(a) Consider a state table with three states to be realized using three J-K flip-flops. To be sure of getting the minimum amount of logic, how many different state assignments must be tried? Enumerate these assignments.

(b) For four states and three flip-flops, 29 assignments must be tried. Enumerate 10 of these, always assigning 000 to the first state.

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