Physical Limits of Computing Dr. Mike Frank CIS 6930, Sec. #3753X Spring 2002

1. Physical Limits of ComputingDr. Mike Frank CIS 6930, Sec. #3753XSpring 2002 Lecture #23Adiabatic Electronics & CMOS Mon., Mar. 11

2. Administrivia & Overview • Don’t forget to keep up with homework! • We are 7 out of 14 weeks into the course. • You should have earned ~50 points by now. • Course outline: • Part I&II, Background, Fundamental Limits - done • Part III, Future of Semiconductor Technology - done • Part IV, Potential Future Computing Technologies - done • Part V, Classical Reversible Computing • Fundamentals of Adiabatic Processes & logic - last Wed. & Fri.(----------------------- Spring Break ------------------------) • Adiabatic electronics & CMOS logic families - TODAY • Limits of adiabatics: Leakage and clock/power supplies. - Wed. 3/13 • RevComp theory I: Emulating Irreversible Machines - Fri. 3/15 • RevComp theory II: Bounds on Space-Time Overheads - Mon. 3/18 • (plus ~7 more lectures…) • Part VI, Quantum Computing • Part VII, Cosmological Limits, Wrap-Up

3. Adiabatic electronics & CMOS implementations

4. Conventional Gates are Irreversible • Logic gate behavior (on receiving new input): • Many-to-one transformation of local state! • Required to dissipate bT by Landauer principle • Incurs ½CV2 dissipation in 2 out of 4 cases. Transformation of local state: Example: Static CMOS Inverter: in out

7. Exact formula:for frequency reductionf :RC/t

9. Adiabatic Rules for Transistors • Rule 1: Never turn on a transistor if it has a nonzero voltage across it! • I.e., between its source & drain terminals. • Why: This erases info. & causes ½CV2 disspation. • Rule 2: Never apply a nonzero voltage across a transistor even during any onoff transition! • Why: When partially turned on, the transistor has relatively low R, gets high P=V2/R dissipation. • Corollary: Never turn off a transistor if it has a nonzero current going through it! • Why: As R gradually increases, the V=IR voltage drop will build, and then rule 2 will be violated.

10. Adiabatic Rules continued • Transistor Rule 3: Never suddenly change the voltage applied across any on transistor. • Why: So transition will be more reversible; dissipation will approach CV2(RC/t), not ½CV2. Adiabatic rules for other components: • Diodes: Don’t use them at all! • There is always a built-in voltage drop across them! • Resistors: Avoid moderate network resistances. • e.g. stay away from range >10 k and <1 M • Capacitors: Minimize, reliability permitting. • Note: Dissipation scales with C2!

11. Transistor Rules Summarized Legal transitions in green. (For n- or p-FETs.)Dissipative states and transitions in red. off high low off off high high low low off low high on on low high high low on on low low high high

12.  Transformation of local state:

13. Input-Barrier, Clocked-Bias Retractile * Must reset outputprior to input.* Combinational logiconly! • Cycle of operation: • Inputs raise or lower barriers • Do logic w. series/parallel barriers • Clock applies bias force which changes state, or not 0 0 0 Examples:Hall’s logic,SCRL gates,Rod logic interlocks Input barrier height N 1 0 Clocked force applied 

15. Retractile Logic w. SCRL gates • Simple combinational logic of any depth N: • Requires N timing phases • Non-pipelined • No sequential reuse ofHW (even worse) • Sequential logicis required! Time 

16. Sequential Retractile Logic • Approach #1 (Hall ‘92): • After every N stages, invoke an irreversible latch • stores the output of the last stage • Then, retract all the stages, • and begin a new cycle • Problems: • Reduces dissipation by at most a factor of N • Also reduces HW efficiency by order N! • In worst case, compared to a pipelined, sequential circuit • Approach #2 (Knight & Younis, ‘93): • The “store output” stage can also be reversible! • Gives fully-adiabatic, sequential, pipelined circuits! • N can be as small 1 or 2 & still have arbitrarily high Q

17. P Simple Reversible CMOS Latch • Uses a standard CMOS transmission gate • Sequence of operation: (1) input initially matches latch contents (output) (2) input changesoutput changes (3) latch closes (4) input removed Before Input Inputinput: arrived: removed:inoutinoutinouta a a a a a b b a b P in out

18. Resetting a Reversible Latch • Can reversibly unlatch data as follows: (exactly the reverse of the latching process) • (1) Data value d stored on memory node M. • (2) Present an exact copy of d on input. • (3) Open the latch (connecting input to M). • No dissipation since voltage levels match • (4) Retract the copy of d from the input. • Retracts copy stored in latch also.

19. Input-Bias Clocked-Barrier Logic • Cycle of operation: • Data input applies bias • Add forces to do logic • Clock signal raises barrier • Data input bias removed Can amplify/restore input signalin clocking step. Retractinput 1 1 Retractinput Clockbarrierup Can reset latch reversibly givencopy of contents. 0 0 Clock up Input“1” Input“0” Examples: AdiabaticQDCA, SCRL latch, Rod logic latch, PQ logic,Buckled logic N 1 0

22. SCRL 6-tick clock cycle Initial state: All gates off, all nodes neutral. in out

23. SCRL 6-tick clock cycle Tick #1: Input goes valid, forward T-gate opens. in out

24. SCRL 6-tick clock cycle Tick #2: Forward gate charges, output goes valid.(Tick #1 of subsequent gate.) in out

25. SCRL 6-tick clock cycle Tick #3: Forward T-gate closes, reverse gate charges. in out

26. SCRL 6-tick clock cycle Tick #4: Reverse T-gate opens, forward gate discharges. in out

27. SCRL 6-tick clock cycle Tick #5: Reverse gate discharges, input goes neutral. in out

28. SCRL 6-tick clock cycle Tick #6: Reverse T-gate closes, output goes neutral.Ready for next input! in out

29. 24 ticks/cyclein this version-includes 2-levelretractile stages

32. Some Interesting Questions • About pipelined, sequential, fully-adiabatic CMOS logic: • Q: Does it require these intermediate voltage levels? • A: No, you can get by with only 2 different levels. • Q: What is the minimum number of externally provided timing signals you can get away with? • A: 4 (12 if split levels are used) • Q: Can the order-N different timing signals needed for long retractile cascades be internally generated within an adiabatic circuit? • A: Yes, but not statically, unless N2 hardware is used • where N is the number of stages per full sequential cycle • We now demonstrate these answers.

33. P 2LAL: 2-level Adiabatic Logic P P • Use simplified T-gate symbol: • Basic buffer element: • cross-coupled T-gates • Only 4 timing signals,4 ticks per cycle: • i rises during tick i • i falls during tick ((i+1) mod 4)+1 : 2 Tick # in 1 2 3 4 1 2 out 3 1 4

34. 2LAL Cycle of Operation 21 in1 in0 20 out1 in 11 10 21 in=0 out0 out=0 11 10

35. Shift Register Structure • 1-tick delay per logic stage: • Logic pulse timing & propagation: 2 3 4 1 in out 1 2 3 4 1 2 3 4 ... 1 2 3 4 ... in in

36. More complex logic functions • Non-inverting Boolean functions: • For inverting functions, must use quad-rail logic encoding: • To invert, justswap the rails! • Zero-transistor“inverters.”   A B A A B AB AB A = 0 A = 1 A0 A0 A1 A1

37. Hardware Efficiency issues • Hardware efficiency: How many logic operations per unit hardware per unit time? • Hardware spacetime complexity: How much hardware for how much time per logic op? • We’re interested in minimizing:(# of transistors) × (# of ticks) / (gate cycle) • SCRL inverter, w. return path: • (8 transistors)  (6 ticks) = 48 transistor-ticks • Quad-rail 2LAL buffer stage: • (16 transistors)  (4 ticks) = 64 transistor-ticks

38. More SCRL vs. 2LAL • SCRL reversible NAND, w. all inverters: • (23 transistors)  (6 ticks) = 138 T-ticks • Quad-rail 2LAL AND: • (48 transistors)  (4 ticks) = 192 T-ticks • Result of comparison: Although 2LAL minimizes # of rails, and # ticks/cycle, it does not minimize overall spacetime complexity. • The question of whether 6-tick SCRL minimizes per-op spacetime complexity among pipelined adiabatic CMOS logics is still open.