Hardware Reference
In-Depth Information
Figure 1.8
(a) State machine containing all four types of transitions (from a hardware perspective):
condi-
tional
,
timed
,
conditional-timed
, and
unconditional
. (b) A special
compound
transition, which checks
whether a condition has been true
during the whole time
.
cycles. This implies that it will remain in state C during
at least T
2
clock cycles, not
necessarily during exactly
T
2
clock cycles.
Transition DA
(unconditional transition)
is the simplest type of transition. The
machine must move from state D to state A at the next (positive) clock edge, regard-
less of
x
and
t
, thus staying in D during exactly one clock period.
Note that even though
t
denotes time in the description above, it is not expressed
in seconds but rather in “number of clock cycles.” For example, if we want the
machine to stay in a certain state during
t
state
= 2 ms, and the clock frequency is
f
clk
= 50 MHz, we simply adopt
T
state
=
t
state
50·10
6
= 100,000 clock cycles.
A special time-dependent transition is shown in i gure 1.8b. Note that the
conditional-timed transition CD in i gure 1.8a only checks if
x
=
x
2
after
T
2
clock cycles.
Say, however, that we want the machine to move from C to D only if
x
=
x
2
has
occurred
during the whole time
(i.e., during all
T
2
clock cycles). To cover this case, a
compound
transition is needed that results from the combination of three pure transi-
tions, as shown in i gure 1.8b. This arrangement works well because the timer is zeroed
every time the machine changes its state. Note that
T
2
×
f
clk
= 2·10
-3
×
1 clock cycles are needed in
the XD transition (so the timer must count from 0 to
T
2
−
2) because one clock cycle
is spent in the CX transition. Even though in many applications this “
−
−
2” factor in
t
=
T
2
2 is not relevant, it is maintained here for the sake of accuracy. Much more on
time-dependent transitions is presented in chapter 8.
In section 3.6, the transition types described above are used to classify any hardware-
implemented FSM into one of the following three categories:
regular machines
,
timed
machines
, or
recursive machines
. Two fundamental decisions must then be made when
developing an actual design in hardware: the machine category (just listed) and the
machine type (Moore or Mealy).
−
1.7 Moore-to-Mealy Conversion
Moore machines can be converted into corresponding Mealy machines. The latter will
have the same number of states as the former if state merging is not possible, or fewer
states otherwise.
