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Asynchronous Machines. Used slides from Mitch Thornton and Prof. Hintz. Reduce States. State Assignment. Flip-Flop or Latch Selection. Asynchronous FSM. Fundamental Mode Assumption Only one input can change at a time

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Asynchronous Machines

- Used slides from Mitch Thornton and Prof. Hintz

Asynchronous FSM

Fundamental Mode Assumption

- Only one inputcan change at a time
- Analysis too complicated if multiple inputs are allowed to change simultaneously

- Circuit must be allowed to settle to its final value before an input is allowed to change
- Behavior is unpredictable (nondeterministic) if circuit not allowed to settle

Asynch. Design Difficulties

Delay in Feedback Path

- Not reproducible from implementation to implementation
- Variable
- may be temperature or electrical parameter dependent within the same device

- Analog
- not known exactly

Tell my stories how I worked with asynchronous machines in 1968

Stable State

- PS = present state
- NS = next state
- PS = NS = Stability
- Machine may pass through none or more intermediate states on the way to a stable state
- Desired behavior since only time delay separates PS from NS

- Oscillation
- Machine never stabilizes in a single state

Races

- A Race Occurs in a Transition From One State to the Next When More Than One Next State Variables Changes in Response to a Change in an Input
- Slight Environment Differences Can Cause Different State Transitions to Occur
- Supply voltage
- Temperature, etc.

Types of Races

- Non-Critical
- Machine stabilizes in desired state, but may transition through other states on the way

- Critical
- Machine does not stabilize in the desired state

11

00

10

00

critical race

RacesPS

if Y2 changes first

if Y1 changes first

desired NS

non- critical race

Asynchronous FSM Benefits

- Fastest FSM
- Economical
- No need for clock generator

- Output Changes When Signals Change, Not When Clock Occurs
- Data Can Be Passed Between Two Circuits Which Are Not Synchronized
- In some technologies, like quantum, clock is just not possible to exist, no clocks in live organisms.

Next State Variables

You can analyze this machine at home

Asynchronous State Tables

States are either Stable or Unstable.

Stable states encircled with symbol.

Oscillations occur if all states are unstable for an input value.

Total Stateis a pair (x, Qi)

Constraints on Asynchronous Networks

If the next input change occurs before the previous ones effects are fed back to the input, the machine may not function correctly.

Thus, constraints are needed to insure proper operation.

Fundamental Mode – Input changes only when the machine is in a stable state.

Normal Fundamental Mode – A single input change occurring when the machine is in a stable state produces a single output change.

Example 8.4

Find state table for network

Let Q0 be state when y1 = 0 and Q1 be state when y1 = 1.

z1z2

Example 8.5

Analyze circuit without fundamental mode

Example 8.6 (Continued)

Use S when state variable must change from 0 to 1

Use R when state variable must change from 1 to 0

Use s when state variable remains 1

Use r when state variable remains 0

Example 8.7 – D Flip-Flop

Design the circuit from the state table using SR-latches

Example 8.8

Derive the state table from the circuit

1’s where Set and (present state is 1 and not R)

Race Conditions - Example 8.9

Race Condition – when two or more variable change at a time

Critical Race – final state dependent on order in which the state variables change

Input x1,x2 10 00

10, 00, 01 ok

10, 11, 01 not ok.

Q3

Q2

Avoiding RaceState Adjacency Diagram

State Adjacency Diagram

Q0

Q1

Impossible to have hamming distance of 1 between all adjacent states. Must add states.

Table from previous page

Asynchronous Machine Hazards

Steady-State Hazards– Occurs when a sequential network goes to an erroneous state due to gate delay.

Static-1 Hazard

In (01, Q1) consider input change (00) (01)

y1= x1x2 +x1 y1y2+x2 y1y2

y2 = x1x2 +x2 y2+x1y1

Steady-State Hazards

Elimination of Static-1 Hazard

y1= x1x2 +x1 y1y2+x2 y1y2

y2 = x1x2 +x2 y2+x1y1 +x1 y2

Hazard Example Feedback Sequential Implementation

Maps resulting from State Table 8.5, Example 8.7

Essential Hazard

- Essential Hazard–
- Erroneous sequential operation that cannot be eliminated without controlling delays in the circuit.
- Not affected by elimination of combinational logic hazards.

Essential Hazard Example

Caused by multiple paths for x

Starting in stable stateQ2 with input 0 1

Slow

Students should complete this example in class, on Friday or at home

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