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350
8.5.
Unit 5 – State Machines & Sequential Components
1.
We should find the state diagram following the steps in the class notes
a.
Find the excitation equations for D
0
and D
1
.
D
0
= Q
1
·
Y + Q
0
·
X
D
1
= Q
1
’
·
Q
0
’
·
X
b.
Find the transition equations using D Flipflops.
According to the characteristic equation of the D Flipflop, we get the
transition equations below:
Q
0
*
= Q
1
·
Y + Q
0
·
X
Q
1
*
= Q
1
’
·
Q
0
’
·
X
c.
The equation for outputs of the state machine is:
Z = Q
0
·
X
d.
Construct transition/output table
Current
State
Next State
Output
XY= 00
XY= 01
XY= 10
XY= 11
XY=00 XY=01
XY=10
XY=11
Q
1
Q
0
Q
1
*
Q
0
*
Q
1
*
Q
0
*
Q
1
*
Q
0
*
Q
1
*
Q
0
*
Z
Z
Z
Z
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
e.
Substitute symbolic state names for the codes.
Current
State
Next State
Output
XY= 00
XY= 01
XY= 10
XY= 11
XY=00 XY=01
XY=10
XY=11
State
Next
State
Next
State
Next
State
Next
State
Z
Z
Z
Z
SA
SA
SA
SC
SC
0
0
0
0
SB
SA
SA
SB
SB
0
0
1
1
SC
SA
SB
SA
SB
0
0
0
0
SD
SA
SB
SB
SB
0
0
1
1
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f.
Draw the state diagram
2.
First, we should find the state diagram following the steps in the class notes.
a.
Find the excitation equations for J0, J1, K0 and K1.
J
0
= Restart’
K
0
= 1
J
1
= Q
0
·
Restart’
K
1
= Restart + Q
0
b.
Find the transition equations using JK Flipflops.
According to the characteristic equation of the JK Flipflop, we get the
transition equations below:
Q
0
*
= J
0
·
Q
0
’
+ K
0
’
·
Q
0
= Restart’
·
Q
0
’
Q
1
*
= J
1
·
Q
1
’
+ K
1
’
·
Q
1
= Q
0
·
Restart’
·
Q
1
’
+ Q
0
’
·
Restart’
·
Q
1
c.
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This note was uploaded on 06/23/2008 for the course EE 101 taught by Professor Redekopp during the Fall '06 term at USC.
 Fall '06
 Redekopp

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