1. 7.4 Clocked Synchronous State-Machine Analysis
Introduction
The goal of a sequential circuit analysis is to determine the next-state and output functions so that the behavior of a circuit can be predicted.
In this section, we will discuss how to analyze a clocked synchronous state-machine. It’s one of the main emphases in this course.
Turn-the-crank
The characteristic is that the steps for analyzing a clocked synchronous state-machine are almost the same. So, it will become very simple if we have learned the basic principles.
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2. 7.4 Clocked Synchronous State-Machine Analysis
Specialized Words
flip-flop 触发器
excitation equation 激励（驱动）方程
transition/state equation 转移/状态方程
output equation 输出方程
characteristic equation 特性（征）方程
transition table 转换表
state table 状态表
state/output table 状态/输出表
state diagram 状态图
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3. 7.4 Clocked Synchronous State-Machine Analysis
Review
1. What are the two types the state-machine structure include? What characteristic does it have for each one?
Mealy machine
Moore machine
Z = G (Q n, X )
Z = G (Q n)
2. What are the excitation equation, transition equation, and output equation ?
Output equation
Excitation equation
Transition equation
Next-state logic F
State memory input W
Output logic G
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4. 7.4 Clocked Synchronous State-Machine Analysis
3. Please write the characteristic equations of D flip-flop and J-K flip-flop.
D flip-flop Qn+1= D
J-K flip-flop Qn+1= J·Qn+K·Qn
7.4.1 Analysis of State Machines with D Flip-Flops
The analysis has three basic steps:
1. Determine the next-state and output functions F and G.
2. Use F and G to construct a state/output table that completely specifies the next state and output of the circuit for every possible combination of current state and input.
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5. 7.4 Clocked Synchronous State-Machine Analysis
3. Draw a state diagram that presents the inform-ation from the previous step in graphical form. Q0 Q1 D0 D1
Example I
MAX=Q1·Q0·EN
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6. 7.4 Clocked Synchronous State-Machine Analysis
Excitation equations
Transition equations
How can we obtain the transition equations from the excitation equations?
Output equation
MAX=Q1·Q0·EN
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7. 7.4 Clocked Synchronous State-Machine Analysis1
0 0
0 1
1 0
1 1
Q1 Q0
Transition/output table EN 1 S0 S1 S2 S3 S
State/output table EN
S1 S2 1 1 1
MAX=Q1·Q0·EN
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8. 7.4 Clocked Synchronous State-Machine Analysis1 S0 S1 S2 S3 S
State/output table EN
S1 S2 S0 S1 S2 S3
1/0
0/0
State diagram
1/1 S
EN/MAX
What is the function of the logic circuit ?
It’s a modulo-4 2-bit binary counter with enable.
Simulation
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9. 7.4 Clocked Synchronous State-Machine Analysis
Example II Q0 Q1 Q2 D0 D1 D2
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10. 7.4 Clocked Synchronous State-Machine Analysis
Excitation equations
Transition equations
Output equation
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11. 7.4 Clocked Synchronous State-Machine Analysis
Transition/output table
0 1
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Q2Q1Q0
0 0 XY
1 1
1 0
Z1Z2
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12. 7.4 Clocked Synchronous State-Machine Analysis
State/output table s0 s1 s2 s3 s4 s5 s6 s7 S 00 XY
Z1Z2
1 0
0 0
1 1 01 11 10
State diagram S0 S1 S3 S2
1x/10
0x/10 S
XY/Z1Z2 S5 S6 S7 S4
1x/00
01/10
xx/11
0x/00
00/10
xx/10
Simulation
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13. 7.4 Clocked Synchronous State-Machine Analysis
7.3.3 Analysis of State Machines with J-K Flip-Flops Q0 Q1 Q2 J0 J1 J2 K0 K1 K2
Excitation equations
Transition equations
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14. 7.4 Clocked Synchronous State-Machine Analysis
Transition/output table
Q2 Q1 Q0 1 C
State diagram
Q2Q1Q0 /C
000
001
010
011
100
111
110
101 /1 /0
Simulation
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15. 7.4 Clocked Synchronous State-Machine Analysis
Summary
The detailed steps for analyzing a clocked synchronous state machine are as follows:
1. Determine the excitation equations.
2. Determine the transition equations.
3. Determine the output equations.
4. To construct a transition/output table.
5. To construct a state/ output table.
6. (Optional) Draw a state diagram.
Exercises
P647~ , 7.15, 7.16, 7.17, 7.18, 7.19
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