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A sequence detector
A state machine is required which outputs a logic 1 whenever the
input sequence 0101 is
detected, and which outputs a otherwise. The input is supplied
serially, one bit at a time.
The following is an example input sequence and output
sequence:
input 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0
output 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0
This state machine can be designed in a straightforward way.
Assume that the machine is
initially in some state, say, state A. f a 0 is input, then this
is maybe the start of therequired sequence, so the machine should
output a 0 and go to the next state, state !. f a
1 is input, then this is certainlynot the start of the required
sequence, so the machine
should output a 0 and stay in state A. "hen the machine is in
state A, therefore, it has
detected no digits of the required input sequence. "hen the
machine is in state !, it hasdetected exactly one digit #the first
0$ of the required input sequence.
f the machine is in state ! and a 0 is input, then two
consecutive 0%s must have been
input& this input is clearly not the second digit of the
required sequence, but it may be the
first digit of the sequence. Therefore, the machine should stay
in state ! and output a 0. f
a 1 is input while the machine is in state !, then the first two
digits of the requiredsequence have been detected, and the machine
should go to the next state, state ', and
output a 0. "hen the machine is in state ', it has detected
exactly two digits #0 1$ from
the required sequence.
f the machine is in state ' and a 0 is input, then three digits
of the required sequencehave been input, so the machine should go
to its next state, state (, and output a 0. f a 1
is input when the machine is in state ', then this input is
clearly no part of the required
sequence, so the machine should start over in state A and output
a 0.
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f the machine is in state ( and a 0 is input, then this is not
the required input #the input
has been 0 1 0 0$, but this may be the first digit of another
sequence, so the machine
should go to state ! and output a 0. f a 1 is input while the
machine is in state (, then therequired sequence #0 1 0 1$ has been
detected, so a 1 should be output. )oreover, the last
two digits input may be the first two digits of another
sequence, so the machine should go
to state '. This completes the state diagram, as shown in the
following figure:
The following is a state table corresponding to the state
diagram:
*resent nput +ext utput
-tate -tate
A 0 ! 0
A 1 A 0
! 0 ! 0
! 1 ' 0
' 0 ( 0
' 1 A 0
( 0 ! 0
( 1 ' 1
