Hardware Reference
In-Depth Information
A corrected version for the overspecii ed machine of i gure 1.6a is presented in
i gure 1.6b. In this example the following priority list was adopted (from highest to
lowest): AB, AC, AA.
Figure 1.6c shows another example of overspecii cation. The transition control
signals now are
a
,
b
, and
c
. The AB transition is governed by the condition
a
= '1' and
thus covers the cases
abc
= “1
” = {“100”, “101”, “110”, “111”}. The AC transition
is governed by the condition
b
= '1' and thus covers the cases
abc
= “
−
−
” = {“010”,
“011”, “110”, “111”}. Similarly, the AD transition is governed by the condition
c
= '1'
and thus covers the cases
abc
= “
−
1
−
1” = {“001”, “011”, “101”, “111”}. Note that several
conditions are repeated, causing conl icts. To solve the problem, we must again estab-
lish priorities.
A corrected version for the overspecii ed machine of i gure 1.6c is presented in
i gure 1.6d. In this example the following priority list was adopted (from highest to
lowest): AB, AC, AD, AA.
In summary, the outward transition conditions must be
exactly fully complementary
.
In other words, they must include all possible combinations of the transition control
signals, but without any repetitions.
In regard to underspecii cation, another example is shown in i gure 1.7, in which
an integer
t
, produced by a counter to represent time, is the transition control signal.
The machine must stay in state A during
T
clock periods, moving then to state B.
Because the timer's initial value is zero, it must count from 0 to
T
−
−
−
1 in order to span
T
clock cycles, which is the reason why
t
=
T
1 (instead of
t
=
T
) appears in the transi-
tion control conditions (specii c details on timed transitions are given in chapter 8).
Note in i gure 1.7a that the outward transition conditions from state A are not truly
complementary because the
t
−
>
T
−
1 condition is not covered. It was i xed in i gure
1.7b with the
t
1 condition associated with the AB transition. Another corrected
option is shown in i gure 1.7c, this time with the
t
>
T
−
>
T
−
1 condition associated with
the AA transition.
There are two main reasons for not using non-truly complementary conditions.
First, the machine can go into an undesirable state, even get deadlocked (for example,
if the initial state is A and the timer is not properly reset, starting with
t
>
T
−
1,
Figure 1.7
Noncomplementary transition conditions. (a) Condition
t
>
T
−
1 not covered. (b, c) Corrected
versions with
t
>
T
−
1 associated with the AB and AA transitions, respectively.
