Derive the state graph and table for a Moore sequential

Chapter 14, Problem 14.3

(choose chapter or problem)

Derive the state graph and table for a Moore sequential circuit which has an output of 1 iff (1) an even number of 0’s have occurred as inputs and (2) an odd number of (non overlapping) pairs of 1’s have occurred. For purposes of this problem, a pair of 1’s consists of two consecutive 1’s. If three consecutive 1’s occur followed by a 0, the third 1 is ignored. If four consecutive 1’s occur, this counts as two pairs, etc.

(a) The first step is to analyze the problem and make sure that you understand it. Note that both condition (1) and condition (2) must be satisfied in order to have a 1 output. Consider condition (1) by itself. Would condition (1) be satisfied if zero 0’s occurred? ___________

If one 0 occurred? ___________ Two 0’s? ___________ Three 0’s? _________.

(Hint: Is zero an even or odd number? ___________)

(b) How many states would it take to determine if condition (1) by itself is satisfied, and what would be the meaning of each state?

     _______________________________________________________________

(c) Now consider condition (2) by itself. For each of the following patterns, determine whether condition (2) is satisfied:

010___________           0110___________         01110___________

011110___________     01010___________       011010___________

0110110___________

Now check your answers to (a), (b), and (c).

(d) Consider condition (2) by itself and consider an input sequence of consecutive 1’s. Draw a Moore state diagram (with only 1 inputs) which will give a 1 output when condition (2) is satisfied. State the meaning of each of the four states in your diagram (for example, odd pairs of 1’s).

(e) For the original problem, determine the sequence for Z for the following example:

X = 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0

Z = 0 ________________________________

(f ) Considering that we must keep track of both even or odd 0’s, and even or odd pairs of 1’s, how many states should the final graph have? ______________

(g) Construct the final Moore state graph. Draw the graph in a symmetric manner with even 0’s on the top side and odd 0’s on the bottom side. List the meanings of the states such as

\(S_0\) = even 0’s and even pairs of 1’s.

(h) Check your answer using the test sequence from part (e). Then, check your answers below.