CIRCUITS
(; ::r~
SEQUENTIAL ,ctey
~
~
%1
XI~
fx-ky~
~
%1 In output
variables
" input X1
variables
%",
XII
Combinational
circuit
YI
k secondary
variables
(present
state)
Ya
Y1
Y2 .
.::
k variables
excitation
I
(next state)
Y/c
.
: Y/c
LAd
,
~~
T~kf'
* Content of k memory cells
e.g., k = 3
~
[] [] []
=STATE
of the sequential circuit
* Since each memory cell stores one bit (0 or 1),
there are 2k possible states of the sequential circuit
e.g., k = 3
~
23possible states
~
23possible contents of 3 memory cells
~
000, 001, 010, 011, 100, 101, 110, 111
.
* present content of k memory cells = PRESENTSTATE~ YlY2 ."Yk
STATE ~
Y 1Y2 ...Yk
* next
content of k me.morycells = NEXT
* z.
1
y.J
= f(Yl' Y2' ..., Yk' Xl' X2' ..., xn), 1 < i < m
= f(Yl' Y2' ..., Yk' Xl' X2' ..., xn)' 1 <j < k
~~~
e.g.,
E vt ~
~r
x
"
vvt;"
c~
r
c~'ovt
'/
uJ1
z
bl ~oJ[~
~
80
.JJ
z= R (11"iZ'X:)
Y, =
fA C'<I, 'J } x)
2.
h
c: ..,c.v.:.t
f3 (~I ) ~~}
)
~
n.t7<+
fl~
)
x
~
:
b,J-Nk
.'
'ASYNCHRONOUS
SEQUENTIAL CIRCUITS
RESPONDS TO A CHANGE INONE OF THE INPUTS
OPERATES IN THE FUNDAMENTAL MODE:
(input signals change one at a time and only when the circuit is in a stable state)
~
d: ::: y~
MEMORY ELEMENTS: LATCHES
0
U
0
0
1
0
1
to
0
I
Q'
R
1
Q
R
SR-IAA~
[, -FJ'kCK I~)
l~ef)
I
S
)
\8.-/4\~+
0
I
0
0
Q
.
Q'
0 I.
<;;e+S
0
(AnerSR
.
fCuet
I
0
(Anc:rSR .01)
{'M
W\
Crossc~.&:Oupl&:~
circuit
f C';b -: R \
;-c.'t r;~
C(S+~)/-rR)
:= ~T'(f)R,
f.
.';
~
"
-
~R' +-
1(6'
~t
"J
(N't U
~~Y\~r.eA
.~Ve,
lvz-
tt..J-
i
~
5
~
Circalit showinG rc&:~back
bc1t
R}.
S
-
'JCJIEEI
~
.p..
10)
11
s
R
I f L~ k
~
I
,,= S + R~
8t
SYNCHRONOUS
SEQUENTIAL
CIRCUITS
RESPONDS TO THE CLOCKPULSE Cc.p)
~
MEMORY ELEMENTS: FLlPFLOPS
s
Q
c foCK rv.l~
CP
a'
R
(a) Logic dingnll11
SR
ri~RMf
/
I . 0(1 + .1)
Q(/)
0
1
?
No change
Reset
Set
Unpredictable
R
0
0
0
0
I
I
0
0
I
I
0
0
0
I
0
I
0
I
I
.0
I
0
1
0
1
Q[J.)S
I
0
0
1
1
.
V'
I
I
s../-fJe
r\ s i>d- t-Ie.
Q
Q(/+I)
0
0
I
Indeterminate
I
0
A.
01
II
a{
I
~
x
y
R
I
Indeterminate
~
(lei
+ I)"
SR"O
S
Q
CP
Q'
(a) Logic dingrum
D
D
OCt+ I)
0
1
0
1
0
olV I) Q(f + I)
Reset
Set
000
0II
I00
III
1
0
o( I
OCt+ 1)-0
(b) Characteristic table,
+ R'Qlf)
(c) Chur.actcristic: Ctluation
5-=-b
D
10
x
0
(b) Characteristic table~
.~
S
SR
00
(c) Characteristic equation
JK-
~
t=t(f~
J'=/
R2..
k~'
f..
~Ct-ti) =
~ Ci)
a
K
CP
a'
J
(a) Logic diagram.
JK
I
OCt+ I)
00
0: 1
10
11
Q(t)
0
1
No change
Reset
Set
Q '(1)
Complement
0
0
0
0
J
1
1
I
J
0
0
J
1
0
0
1
1
K
0
1
0
1
0
J
0
J
a (I + I)
0
0
J
1
1
0
J
0
J
JK
Q 00
11
01
0
- 10
.
11
1I
- JQr~
K'Q[+)
O{I
K
Q(I
+
J)
(c) Characteristicequation
(b) Characteristictables
T ~~tP~
5:t Y'~
~r..,J-
1: "J'K- FF.
~
y-ey4i VY)
-,~ '.1
~[t+,)
~
T
Q
,
@ C+)
CP
Q'
(a) Logic diagram
T
OCt+ I)
0
I.
Q(/)
Q '(1)
No change
Complement
-_.
Q(~T
000
0J
10
11
(b) Char:lctcristic tables
QCt+ I)
1
1
0
T
0
0
1
I
I
Q! I
QCt+ 1)- TQ~ T'Q(+)
(c) Characteristicequation
.s.et.-.J.t~
4.[)
~3
l{.2.} 4,3
FLIP FLOP CHARACTERISTIC TABLES
.
Flip-Flop Characteristic
-
Tables
-----
JK Flip-Flop
JK
SR
OCt + I)
00
01
1- 0
11
..
Q(/)
0
1
Q '(1)
I
OCt+ I)
00
01
10
11
No change
Reset
Set
-
Compleri1en t
Q(t)
0
1
?
D Flip-Flop
D
0
1
GtiV.ef\
Unpredictable
T Flip-Flop
----.-.--.---
OCt + I)
0
1
No change
Reset
Set
T
0
I
Reset
Set
~
f"f..S~
~
Q(/)
Q '(1)
~
~'~
L i"f~;J
OCt + I)
&It)
No change
Complemen t
$-(1:+1)
FLIP FLOP EXCITATIONTABLES
Flip-Flop Excitation
Tables
OCt)
OCt+ J)
S
R
OCt)
O(t+ J)
J
K
0
0
1
1
0
1
0
1
0
1
0
X
X
0
I
0
0
0
1
1
0
1
0
1
0
I
X
X
X
X
. (a) RS
)
0
(b) JK
OCt)
O(t + I)
D
OCt)
O(t + J)
0
0
0
0
1
0
'
0
0
1
1
1
0
1
J
1
I
1
0
'"
(c) D
0
I
l
)
Ct)
OJ
(b) T
L
G1 Vt)
IT
ruler s
@.(f:+0
J
J
r.