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**Unit 13 Analysis of Clocked Sequential Circuits**

Ku-Yaw Chang Assistant Professor, Department of Computer Science and Information Engineering Da-Yeh University

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**Analysis of Clocked Sequential Circuits**

Outline 13.1 A Sequential Parity Checker 13.2 Analysis by Signal Tracing and Timing Charts 13.3 State Tables and Graphs 13.4 General Models for Sequential Circuits 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

State Tables 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

State Graph 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D T flip-flop Q+ = T Q : Plot a next-state map for each flip-flop. Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

First Example 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D T flip-flop Q+ = T Q : Plot a next-state map for each flip-flop. Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. DA = X B’ DB = X + A Z = A B 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D T flip-flop Q+ = T Q : Plot a next-state map for each flip-flop. Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D D-CE flip-flop Q+ = D · CE + Q · CE’ T flip-flop Q+ = T Q S-R flip-flop Q+ = S + R’Q J-K flip-flop Q+ = JQ’ + K’Q A+ = X B’ B+ = X + A 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D T flip-flop Q+ = T Q : Plot a next-state map for each flip-flop. Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Plot a next-state map for each flip-flop. A+ = X B’ B+ = X + A 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D T flip-flop Q+ = T Q : Plot a next-state map for each flip-flop. Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Combine these maps to form the state table. A transition table 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Moore State Graph 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Second Example 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Determine the flip-flop input equations and the output equations from the circuit. JA = XB, KA = X JB = X, KB = XA Z = XB’+XA+X’A’B 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Derive the next-state equation for each flip-flop from its input equations, using one of the following relations: D flip-flop Q+ = D D-CE flip-flop Q+ = D · CE + Q · CE’ T flip-flop Q+ = T Q S-R flip-flop Q+ = S + R’Q J-K flip-flop Q+ = JQ’ + K’Q A+ = JAA’ + KA’A = XBA’ + X’A B+ = JBB’ + KB’B = XB’ + (AX)’B = XB’+ X’B + A’B Z = X’A’B + XB’ + XA 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Plot a next-state and output map. 2004/05/24 Analysis of Clocked Sequential Circuits

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**Construct the State Table**

Combine these maps to form the state table. 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Mealy State Graph 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Third Example Serial Adder xi yi ci ci+1 si 1 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Timing Diagram 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

Serial Adder Initially the carry flip-flop must be cleared C0=0 Start by adding the least-significant (rightmost) bits in each word. Reading the sum output just before the rising edge of the clock 2004/05/24 Analysis of Clocked Sequential Circuits

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**Analysis of Clocked Sequential Circuits**

State Graph A Mealy machine Inputs: xi and yi Output: si Two states represent a carry (ci) S0 for 0 and S1 for 1 2004/05/24 Analysis of Clocked Sequential Circuits

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**Multiple Inputs and Outputs**

2004/05/24 Analysis of Clocked Sequential Circuits

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**Multiple Inputs and Outputs**

2004/05/24 Analysis of Clocked Sequential Circuits

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A sequential logic circuit (a.k.a. state machine) consists of both combinational logic circuit(s) and memory devices (flip flops). The combinational circuits.

A sequential logic circuit (a.k.a. state machine) consists of both combinational logic circuit(s) and memory devices (flip flops). The combinational circuits.

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