Registers

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ECE U322Digital Logic Design
Nov. 3, 2005

• Lecture 24
• Sequential Circuit Design Marcovitz 7.1
• Homework Due Today

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Finite State Machine
Outputs
Nextstatelogic
OutputLogic
Stateregister
Inputs
Moore machine outputs depend on current state
only Mealy machine outputs depend on
current state and inputs
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Sequential Circuit Design

• Procedure
• 1. Specify Obtain state diagram or state table
  based on problem specification
• 2. Write state table if not given in 1
• 3. Determine type and number of flip-flops
• 4. Determine binary codes for states
• 5. Derive flip-flop input equations
• 6. Derive output equations
• 7. Simplify equations from 5 and 6
• 8. Draw logic diagram

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Finding State Diagrams and Tables

• Example Find a state diagram for a sequence
  recognizer.
• Specifications
• Let the input be X and output be Z. Recognize
  the occurrence of the sequence, 01 on X.
• Z 1 when X1 and previous input was 0
• Z 0 otherwise

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States are used to remember something about the
history of past inputs. A state in which none
of the first portion of the sequence has
occurred. B last input was a 0.
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State Table for String Recognizer
Two states one flipflop State A Flipflop
storing 0 State B Flipflop storing 1 Use D
Flipflops
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State Table with Flip-Flops Assigned to States
Input equation What goes on D input to make
next state transition happen D Output
equation What is Z? Z
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Circuit Diagram for Sequence Recognizer
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Timing Diagram for 01 Sequence Recognizer
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More complicated sequence recognizer

• Find a state diagram for an FSM that recognizes
  the sequence 1101
• Let the input be X and output be Z. Recognize
  the occurrence of the sequence, 1101, on X.
• Z 1, when X1 and previous 3 inputs were
  110.
• Z 0, otherwise.
• X 10110101011010110111011101
• Z

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How about non-overlapping Case
Use states to remember past events.
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State Table
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(No Transcript)
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Given sequence 00111011, determine output
sequence and state transitions.
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State Table with State Assignmentoverlapping
sequence recognizer
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Flip-flop and output equations
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Circuit Diagram for Sequence Recognizer
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This is an overlapping sequence recognizer

• X 1101101 ...
• Z 0001001 ...
• The fourth input 1 is the last bit of the first
  recognized sequence and the first bit of the
  second recognized sequence
• I can also have non-overlapping recognizers
• X 1101101101 ...
• Z 0001000001 ...

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State Diagram for non-overlapping sequence
recognizer
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Moore Machine

• Any Mealy machine can be turned into a Moore
  machine, and vice versa
• A Moore machine has the same number of states or
  more states than a Mealy machine
• Output timing is different between a Moore
  machine and a Mealy Machine
• Moore outputs change on clock edge
• Mealy machine output changes whenever inputs
  change

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01 Sequence Recognizer
Mealy machine
Moore machine
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State Table for 01 Recognizer
Output State A State B State C
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State Table for 01 Recognizer

• A 00, B 01, C 10

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Equations for 01 String Recognizer

• D1
• D0
• Z

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Circuit for 01 String Recognizer Moore version
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Timing Diagram for 01 string recognizer Moore
version