Self-Timed SystemsSelf-Timed Systems

• Timing complexity growing in digital design

- Wiring delays can dominate timing analysis (increasing interdependence between logical and physical views of system)

- Low-skew clock distribution consumes power and space

• Self-Timed SystemsSelf-Timed Systems – systems that operate without clocks at speeds determined by their own internal parameters (also know as Delay-Insensitive Systems)

- requires completion signal feedback to the input source

Mitch ThorntonMitch Thornton

Simple Handshake ExampleSimple Handshake Example

SubsystemP2

SubsystemP1

Data

Request (R)

Acknowledge (A)

Four-Phase Handshake

Two-Phase Handshake

Request (R)

Acknowledge (A)

Request (R)

Acknowledge (A)

P1 says “send data” P1 says “send data”

P2 says “data available” P2 says “data available”

P1 says “send data”

P2 says “data available”

Return to 0

Return to 0

How to Apply to Clocked Systems?How to Apply to Clocked Systems?

Phased Logic Concepts

• Completion signalCompletion signal not restricted to simple handshake between two subsystems (rather a system with multiple feedback circuits)

• Conventional clocked systems can be replaced with networks of Phased Logic Gate Primitives that carry both time and value information simultaneously

• Clock (t) and Value (v)

- Encoding scheme used is Level-Encoded two-phase Dual-Rail (LEDR) scheme.

- Four-phase encoding avoided – no resetting transition that consumes power

LEDR Encoding

Level-Encoded two-phase Dual-Rail scheme.

Phased Logic AND GateGate firesGate fires when phases of inputs match phase of gate

Normal output has opposite phase of gate

Arcs A & B: gate cannot “fire” until inputs reach proper phase

Arcs C & D: changes cannot occur until after gate has fired

Phase Logic Gate Timing with Multiple Outputs

Arc A: inputs can change as soon as any output changes phase

Arc B: environment of the gate must guarantee that all outputs have changed before gate is reenabled

Phased Logic GatePhased Logic GateFiring RulesFiring Rules

1)1) Internal ConstraintInternal Constraint:

• the gate fires IFF it is enabled (all inputs match phase of gate).

• A requirement of the gate design.

2)2) External ConstraintExternal Constraint:

• The phase of each input and output toggles once between the nth and (n+1)th firing of the gate.

• A requirement on the system design.

Correspondence Between Phases and Tokens

Example of Token Movement

Initial Token Markings

Live and Safe Initial Token Marking

Phase inversion used to allow live and safe initial token making - output phase the same as the phase of the gate

Liveness and Safety TheoremsLiveness and Safety TheoremsTHEOREM 1.THEOREM 1. A marked graph is live IFF the initial token marking places at least

one token on each directed circuit.

THEOREM 2.THEOREM 2. A live marked graph is safe IFF every edge belongs to some directed circuit with a token count of one in the initial token marking.

Such a circuit is called a synchronizing loop.

Edges violate THM 2

C1 has no token

& violate THM 1

Phased Logic Synthesis

Two Basic Steps:

1) Building Basic Topology- Copy topology of clocked system except for the clock signal

- Each gate replaced with phased logic gate with same function (signals become LEDR)

2) Augmentation to Guarantee Safeness

- Add splitter gates to separate directly connected barrier gates

(gates that have tokens on all its outputs)

- Mark as covered all signals that already safe

- Add feedback to cover the remaining unsafe signals

Phased Logic SynthesisStep 1: Phased logic network for clocked system example

Ordinary signalsSynchronous signals

Tokens on synchronous signals

Phased Logic SynthesisBut step 1 leaves signals circled in red unsafe

Phased Logic Synthesis

Step 2:• Need to augment the network (add new signals and gates) to

guarantee the safeness of all signals.

• But liveness problems can occur when this is done.

Part of unsafe circuit

Created circuit C2

not live

Phased Logic Synthesis

Step 2:

Feedback signal

Splitter gate

Examples of Unsafe signals