A sequential circuit has two inputs, w1and w2, and an output, z. Its function is to compare the input sequences on the two inputs. If w1= w2 during any three consecutive clock cycles, the circuit produces z= 1; otherwise, z= 0. The output should be equal to 1 in the same clock cycle when the third occurrence of w1= w2 is detected.

Answer / Explanation

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A sequential circuit has two inputs w1 and w2, and an output, z. Its function is to compare the

input sequences of the two inputs. If w1=w2 during any four consecutive clock cycles, the

circuit produces z=1; otherwise, z=0.

For example

w1:0110111000110

w2:1110101000111

z:0000100001110

Draw the state diagram using the minimum number of states.

To properly answer this question, let us first define what a sequential circuit is, and input sequence.

To start with,a Sequential circuit can be defined or described as a type of circuit system used in the digital world most importantly in the digital theory of circuits. It is a type of circuit system whose output does not only depends on present values of input signals but also involves the sequence of one or more inputs and one or more outputs of the past whose realities are related.

Input sequence: This can be refereed to as the arranged pattern in which the data or values are imputed in the circuit.

If we now refer back to the question, we have

For grading each state:

+1 for each correct transition                     = 2 total per state

+2 for each correct output                         = 2 total per state

Total for every state                                    = 4

Where the Maximum is  4*5 = 20

Hence,

If more than 5 states are used, but the logic is correct: +10 for the entire answer

Full credits for any other possible solution using 5 states.

We should also understand that : input labeled of (w1 =w2), (w1 == w2), (w1 XOR w2), 00,11 and similar also OK

We should also understand that : The solution here uses more machine. You can also use mealy machine. For mealy  machine, only 4 states are enough. If you use 5 states we don’t deduct points.

So in summary,  X = w1 XOR w2

Kindly find the required diagram below for proper clarity and understanding of the question.

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explanation: