Question

You will design a sequence detector to detect the sequences 010 and 1001. Bits come in series, one at a time. The system must reset after 4 bits come in. Notice that the first sequence, 010 could happen in several ways (e.g., if 0100 comes in or if 0010 comes in... there are others); 1001 may only happen one way.

a) Draw the state transition diagram.

b) From the state transition diagram, create the state transition table.

c) Find obvious equivalent states by looking for repeated rows.

d) Re-write the state transition table using the information from c) (removing redundant states and replacing by their equivalent).

e) Create and fill in the Pairs table to find other equivalences between states.

f) Once you’ve finished (several passes of) the pairs table work, rename your states in consecutive order (either letters or numbers) and write the final state transition table.

g) Re-draw the state transition diagram with fewer states.

Answer 1

Here I have just shown state transition diagram and table.

We have to keep in mind as after getting 4 bits system has to reset ,so we cannot put any self loop!!