EE121 John Wakerly Lecture

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EE121 John Wakerly Lecture 11

• Sequential-circuit design
• Sequential-circuit synthesis

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State-machine design and synthesis

• Example Design a combination lock with two
  inputs, X1 and X2. Open for the sequence X1,
  X2, X2 (one input per clock).

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• Example Design a combination lock with two
  inputs, X1 and X2. Open for the sequence X1,
  X2, X2 (one input per clock).
• Specification ambiguities are resolved in the
  state table.

State X1 X2 --------------------------
----------------------------------------------- Me
aning Name 00 01 10
11 UNLOCK --------------------------
-----------------------------------------------
Start A A A B A 0 Got X1 B A C A A 0 Got
X1,X2 C A D A A 0 Got X1,X2,X2 D A A B A 1
(D)
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State Assignment

• Can minimize number of states (see text), but
  hardly anyone bothers anymore.
• Need to assign state-variable combinations to
  states.
• Minimum number of variables for n states is ?log2
  n?
• Using more than minimum number may be
  advantageous in some situations, e.g., one
  variable per state (one-hot) (see text).
• Example -- 4 states, 2 state variables (Q1,Q2)

A gt 00 B gt 01 C gt 10 D gt 11
Up to this point is art, the rest is just
turning the crank.
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Transition table

• Substitute state-variable combinations for states
  in the state table.

State X1 X2 --------------------------
----------------------------------------------- Me
aning Q1 Q2 00 01 10
11 UNLOCK --------------------------
-----------------------------------------------

----------------------------------------------

Q1? Q2?
Start 0 0 0 0 0 0 0 1 0 0 0 Got X1 0 1 0 0 1 0 0
0 0 0 0 Got X1,X2 1 0 0 0 1 1 0 0 0 0 0 Got
X1,X2,X2 1 1 0 0 0 0 0 1 0 0 1
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Transition equations circuit

• Transition table specifies each state variable
  (Q1?, Q2?) as a combinational logic function of
  Q1, Q2, X1, X2.
• Find a realization of each function by your
  favorite means -- ad hoc, minimal
  sum-of-products, etc.
• Build the circuit.

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Design using ABEL state diagrams
state_diagram LOCKST state A if X1!X2 then B
else A state B if !X1X2 then C else A state
C if !X1X2 then D else C state D if X1!X2
then B else A equations UNLOCK (LOCKSTD)
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Another design example (from text)

• Design a machine with inputs A and B and output Z
  that is 1 if
• A had the same value at the two previous ticks
• B has been 1 since the last time the above was
  true

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State assignment

• There are 6,720 different state assignments of 5
  states to 3 variables.
• And there are even more using 4 or more variables
• Here are a few obvious or interesting ones

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Transition/output table (decomposed assignment)

• Simple textual substitution
• With D flip-flops, excitation table is identical
  to transition table.

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Develop excitation equations

• Assume unused states have next-state 000

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Same example using ABEL

• Note about reset inputs
• You always need a power-on reset input for a
  sequential circuit.
• Previous example did not use synchronous reset
  because of manual-synthesis complexity.
• Asynchronous reset is sometimes used (PR and CLR
  inputs of flip-flops).

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State Diagram
This essentially mimics the state table.
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State assignment

• Note definition of extra states.

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Odds n ends

• Good behavior for extra states
• Clock and output equations
• Alternative state assignments are easy
• Modify state definitions and possibly output pins
  and extra states.
• Unspecified states go to 0,0,0.

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ABEL-derived excitation equations

• Equivalent to what was derived by hand, with the
  addition of the RESET input.

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And now for something completely different...

• ABELs language features can be used to enable a
  different, hybrid approach.
• Use one register to keep track of the previous
  value of A use a state machine for the rest.

Records previous value of A
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Simpler, more natural state machine

• Really an example of state-machine
  decomposition.

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Equations and state assignments
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Wrap-up

• Next time PLD-based state-machine design
  examples
• Discussion of Lab 5
• How to deal with pushbuttons, edge detection,
  etc.