Hardware Reference
In-Depth Information
Fig. 7.4
(
a
) FSM extracted
from the sequential network
of Fig.
7.3
;(
b
) Automaton
that recognizes the language
of the FSM
a
b
1
/
0
10
00
00
−
1
0
/
0
00
0
/
1
−
0
01
dc
01
01
0
/
0
−/
1
−
1
1
/
1
11
−
0
1
/
0
10
11
10
and two latches, with current state variables
cs Dfcs
1
;cs
2
g
and next state variables
ns Dfns
1
;ns
2
g
. The initial state of the latches is state
.00/
. The next state functions
of the latches are
T
1
.i; cs/ D i:cs
2
and
T
2
.i; cs/ D i C cs
1
. The two parts of the
transition relation are
T
1
.i; cs; ns
1
/ D Œns
1
T
1
.i; cs/ D Œns1 i:cs
2
D ns
1
:i:cs
2
C ns
1
:.i C cs
2
/
and
T
2
.i; cs; ns
2
/ D Œns
2
T
2
.i; cs/ D Œns
2
.i Ccs
1
/ D ns
2
:.i Ccs
1
/Cns
2
:i:cs
1
/:
The single output relation is
O.cs
1
;cs
2
;o/ D Œo .cs
1
˚ cs
2
/:
The states of the automaton in Fig.
7.4
b are labeled with the latch values
.cs
1
;cs
2
/
. Transitions (arcs) are labeled with
.i; o/
values. Thus, the transition from
state
.00/
under input
0
is to state
.01/
. The output produced by the network in this
case is
0
. So the label of this transition is
00
(equal to
0=0
using the conventional
FSM labeling, as in Fig.
7.4
a). This automaton is not complete. Thus, the transition
from
.00/
under input
.11/
is not defined. The double-circled states of the automaton
are accepting. The additional (single-circled) state
.DC /
, added for completion, is
not accepting.
DC
has a universal self-loop and all transitions that were originally
undefined (e.g., from
.00/
under input
.11/
) are directed to
DC
.
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