1. Self-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 Thornton

2. Simple Handshake Example Subsystem P2 Subsystem P1 Data Request (R) Acknowledge (A) Four-Phase Handshake Two-Phase Handshake Request (R) Acknowledge (A) Request (R) Acknowledge (A) P1 says “send data” P2 says “data available” P1 says “send data” P2 says “data available” Return to 0

3. How to Apply to Clocked Systems?

4. 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

5. LEDR Encoding Level-Encoded two-phase Dual- Rail scheme.

6. Phased Logic AND Gate Gate fires Gate 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

7. 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

8. Phased Logic Gate Firing Rules 1)Internal Constraint 1)Internal Constraint: the gate fires IFF it is enabled (all inputs match phase of gate). A requirement of the gate design. 2)External Constraint 2)External Constraint: The phase of each input and output toggles once between the n th and (n+1) th firing of the gate. A requirement on the system design.

9. Correspondence Between Phases and Tokens

10. Example of Token Movement

11. Initial Token Markings

12. 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

13. Liveness and Safety Theorems THEOREM 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

14. 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

15. Phased Logic Synthesis Step 1: Phased logic network for clocked system example Ordinary signals Synchronous signals Tokens on synchronous signals

16. Phased Logic Synthesis But step 1 leaves signals circled in red unsafe

17. 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 C 2 not live

18. Phased Logic Synthesis Step 2: Feedback signal Splitter gate Examples of Unsafe signals