Registers; State Machines Analysis

Section 7-1Section 5-4

2

Definition

• Register – a set of flip-flops♦ May include extensive logic to control

state transition♦ register also refers to fast memory for

storing data in a computer

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Simple Register

• Store D = (D0 D1 D2 D3)

• On positive edge of Clock

• Clear signal normally high♦ Power-up reset

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Register with Load Control

• If load signal is H♦ D0 , D1 , D2 , D3

reach inputs of FFs

• If load signal is L, Q is fed back♦ Q0 , Q1 , Q2 , Q3

reach inputs of FFs♦ FFs Keep same

value

5

State Machines: Analysis and Design

• How to design machines that go through a sequence of events

• Basically close this loop

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Analysis of Sequential Circuits

• Earlier we learned how to analyze combinational circuits

• Now extend to synchronous sequential♦ Include time

• We’ll use state tables and state diagrams

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Input Equations: D FF Example

( )AD AX BX

XADB

XBAY )(

Describe inputs to FF with logic equations

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Determining Next State and Output

Current state= {A(t), B(t)} = values stored in FFs during clock t

Next state= {A(t+1), B(t+1) = values stored in FFs during clock t+1}

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Determining Next State and OutputThe current state {A(t), B(t)} & input X are used to determine next state {A(t+1), B(t+1)}( 1)

( ) ( ) ( ) ( ) ( )A

A t

D t A t X t B t X t

( 1)

( ) ( ) ( )B

B t

D t A t X t

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Determining Next State and Output (cont.)

Current state & input X are used to determine output, Y

• Synchronous circuit♦ State transitions are at

positive edge of clock

( ) ( ( ) ( )) ( )Y t A t B t X t

( 1)A t AX BX ( 1)B t AX

( )Y A B X

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State Table

• Just truth table with state added

( 1) ( )AA t D t AX BX ( 1) ( )BB t D t AX XBAY )(

At time tAt time t+1

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Two Dimensional State Table

• Same thing, different layout

)( BXAXDA

XADB

XBAY )(

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Sequential Circuit Types

• Moore model – outputs depend on states

• Mealy model – outputs also depend on inputs

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State Diagram• Alternative representation for

state table• Moore: outputs depend only on

statesState/Output

Inputs

( ) ( 1)AD X Y A A t

Z A

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Mealy Model

• Output depends on input and state Input/Output

State Table for Circuit of Figure 6-17

---------------------------------------------State Table for Circuit of Figure 5-15

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State Table vs. Diagram

• Same information• Table is perhaps easier to fill in

from description• Diagram is easier for

understanding and writing code♦ You can label states with English

description