Unit 13 Unit 13 Analysis of Analysis of Clocked Sequential Clocked Sequential Circuits Circuits Ku-Yaw Chang Ku-Yaw Chang [email protected][email protected]Assistant Professor, Department of Assistant Professor, Department of Computer Science and Information Engineering Computer Science and Information Engineering Da-Yeh University Da-Yeh University
Unit 13 Analysis of Clocked Sequential Circuits. Ku-Yaw Chang [email protected] Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University. Outline. 13.1A Sequential Parity Checker 13.2Analysis by Signal Tracing and Timing Charts - PowerPoint PPT Presentation
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Assistant Professor, Department of Assistant Professor, Department of Computer Science and Information EngineeringComputer Science and Information Engineering
Da-Yeh UniversityDa-Yeh University
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OutlineOutline
13.113.1 A Sequential Parity CheckerA Sequential Parity Checker
13.213.2 Analysis by Signal Tracing andAnalysis by Signal Tracing and Timing Charts Timing Charts
13.3 State Tables and Graphs13.3 State Tables and Graphs
13.4 General Models for Sequential Circuits13.4 General Models for Sequential Circuits
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State TablesState Tables
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State GraphState Graph
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Construct the State TableConstruct the State Table
1.1. Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop QD flip-flop Q++ = D = DT flip-flop QT flip-flop Q++ = T = T Q Q
: :3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.4.4. Combine these maps to form the state table.Combine these maps to form the state table.
A transition tableA transition table
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First ExampleFirst Example
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Construct the State TableConstruct the State Table
1.1. Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop QD flip-flop Q++ = D = DT flip-flop QT flip-flop Q++ = T = T Q Q
: :3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.4.4. Combine these maps to form the state table.Combine these maps to form the state table.
A transition tableA transition table
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Construct the State TableConstruct the State Table
Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
DDAA = X = X B’ B’
DDBB = X + A = X + A
Z = A Z = A B B
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Construct the State TableConstruct the State Table
1.1. Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equationsfrom its input equations, using one of the , using one of the following relations:following relations:
D flip-flop QD flip-flop Q++ = D = DT flip-flop QT flip-flop Q++ = T = T Q Q
: :3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.4.4. Combine these maps to form the state table.Combine these maps to form the state table.
A transition tableA transition table
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Construct the State TableConstruct the State Table
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop D flip-flop QQ++ = D = DD-CE flip-flop D-CE flip-flop QQ++ = D = D ·· CE + Q CE + Q ·· CE’ CE’T flip-flop T flip-flop QQ++ = T = T Q QS-R flip-flop S-R flip-flop QQ++ = S + R’Q = S + R’QJ-K flip-flop J-K flip-flop QQ++ = JQ’ + K’Q = JQ’ + K’Q
AA++ = X = X B’ B’ BB++ = X + A = X + A
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Construct the State TableConstruct the State Table
1.1. Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop QD flip-flop Q++ = D = DT flip-flop QT flip-flop Q++ = T = T Q Q
: :3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.4.4. Combine these maps to form the state table.Combine these maps to form the state table.
A transition tableA transition table
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Construct the State TableConstruct the State Table
3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.
A+ = X B’B+ = X + A
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Construct the State TableConstruct the State Table
1.1. Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop QD flip-flop Q++ = D = DT flip-flop QT flip-flop Q++ = T = T Q Q
: :3.3. Plot a next-state map for each flip-flop.Plot a next-state map for each flip-flop.4.4. Combine these maps to form the state table.Combine these maps to form the state table.
A transition tableA transition table
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Construct the State TableConstruct the State Table
4.4. Combine these maps to form the state table.Combine these maps to form the state table. A transition tableA transition table
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Moore State GraphMoore State Graph
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Second ExampleSecond Example
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Construct the State TableConstruct the State Table
Determine the flip-flop input equations and the Determine the flip-flop input equations and the output equations from the circuit.output equations from the circuit.
JJAA = XB, K = XB, KAA = X = X
JJBB = X, K = X, KBB = XA = XA
Z = XB’+XA+X’A’BZ = XB’+XA+X’A’B
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Construct the State TableConstruct the State Table
2.2. Derive the next-state equation for each flip-flop Derive the next-state equation for each flip-flop from its input equations, using one of the from its input equations, using one of the following relations:following relations:
D flip-flop D flip-flop QQ++ = D = DD-CE flip-flop D-CE flip-flop QQ++ = D = D ·· CE + Q CE + Q ·· CE’ CE’T flip-flop T flip-flop QQ++ = T = T Q QS-R flip-flop S-R flip-flop QQ++ = S + R’Q = S + R’QJ-K flip-flop J-K flip-flop QQ++ = JQ’ + K’Q = JQ’ + K’Q