Hardware Reference
In-Depth Information
Figures 1.4d-g show equivalent representations for the FSM corresponding to the
counter in i gure 1.4c. Because now an external nonoperational input is present (
ena
,
which lets the counter run when high or stops it when low), it can be modeled as
either a Moore or a Mealy machine. However, because counters are inherently syn-
chronous, the Moore approach is the natural choice.
The diagram in i gure 1.4d is the most detailed, expressing, both by name and
numerically, all transition conditions and output values. The representation in i gure
1.4e expresses the transition conditions in Boolean form instead of numeric form.
The representation in i gure 1.4f assumes that
else
is implicit. Finally, the extreme
simplii cation of i gure 1.4g includes just the numeric output values inside the state
circles, assuming again that
else
is implicit. The advantage of the i rst representation
(i gure 1.4d) is that it forces the designer to go over all possibilities more closely,
whereas the advantage of the other representations is a simpler, neater diagram. To
help the reader visualize small details, the i rst representation is used here more often
than the others, but these representations are all equivalent and can be used
interchangeably.
1.5 Under- and Overspecifi ed State Transition Diagrams
This section describes a relatively frequent mistake that occurs while one is preparing
the state transition diagram for a given problem, which consists of either under- or
overspecifying it. An underspecii cation occurs when not all combinations of the
transition control signals are covered, whereas an overspecii cation occurs when one
or more combinations are included more than once.
Figure 1.5a shows an example of underspecii cation. Because the transition control
signals are
a
and
b
, which are single-bit signals, the possible transition conditions are
ab
= {“00”, “01”, “10”, “11”}. In state A, the AA transition is governed by the condi-
tion
a
= '0'; because this is independent of
b
, it is the same as writing
a
= '0' &
b
=
'
” = {“00”, “01”}. The AB transition is governed by
the condition
a
= '1' &
b
= '1', thus covering the case
ab
= “11”. Since there is no
−
', thus covering the cases
ab
= “0
−
Figure 1.5
(a) Example of underspecii ed state transition diagram and (b, c) examples of possible solutions.
In c, the
else
condition is implicit.
