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Physical Limits of Computing Dr. Mike Frank CIS 6930, Sec. #3753X Spring 2002 Lecture #23 Adiabatic Electronics & CMOS Mon., Mar. 11 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 Adiabatic electronics & CMOS implementations 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. Example: Static CMOS Inverter: in out Transformation of local state: Just before transition: in out 0 0 0 1 1 0 1 1 After transition: in out 0 1 1 0 Exact formula: Ediss f 1 f e 1/ f 1 CV 2 for frequency reduction f : RC/t 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 onoff 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. 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! Transistor Rules Summarized Legal transitions in green. (For n- or p-FETs.) Dissipative states and transitions in red. high high off high low low on low high high off low off low off high low on high low on low on high Transformation of local state: Just before transition: After transition: in out 0 ½ 1 ½ in out 0 1 1 0 Input-Barrier, Clocked-Bias Retractile * Must reset output prior to input. * Combinational logic only! • Cycle of operation: – Inputs raise or lower barriers • Do logic w. series/parallel barriers – Clock applies bias force which changes state, or not Examples: Hall’s logic, SCRL gates, Rod logic interlocks 0 0 0 Input barrier height 0 N Clocked force applied 1 Retractile Logic w. SCRL gates • Simple combinational logic of any depth N: – Requires N timing phases – Non-pipelined – No sequential reuse of HW (even worse) • Sequential logic is required! Time 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 Simple Reversible CMOS Latch • Uses a standard CMOS transmission gate • Sequence of operation: (1) input initially matches latch contents (output) (2) input changesoutput changes (3) latch closes (4) input removed P in out P Before input: in out a a Input arrived: in out a a b b Input removed: in out a a a b 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. Input-Bias Clocked-Barrier Logic • Cycle of operation: Can amplify/restore input signal in clocking step. – Data input applies bias • Add forces to do logic – Clock signal raises barrier – Data input bias removed Can reset latch reversibly given copy of contents. Retract input 0 Examples: Adiabatic QDCA, SCRL latch, Rod logic latch, PQ logic, Buckled logic 1 Clock barrier up 0 Clock up Input “0” 0 1 Retract input N Input “1” 1 SCRL 6-tick clock cycle Initial state: All gates off, all nodes neutral. in out SCRL 6-tick clock cycle Tick #1: Input goes valid, forward T-gate opens. in out SCRL 6-tick clock cycle Tick #2: Forward gate charges, output goes valid. (Tick #1 of subsequent gate.) in out SCRL 6-tick clock cycle Tick #3: Forward T-gate closes, reverse gate charges. in out SCRL 6-tick clock cycle Tick #4: Reverse T-gate opens, forward gate discharges. in out SCRL 6-tick clock cycle Tick #5: Reverse gate discharges, input goes neutral. in out SCRL 6-tick clock cycle Tick #6: Reverse T-gate closes, output goes neutral. Ready for next input! in out 24 ticks/cycle in this versionincludes 2-level retractile stages 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. 2LAL: 2-level Adiabatic Logic • Use simplified T-gate symbol: 2 • Basic buffer element: – cross-coupled T-gates • Only 4 timing signals, 4 ticks per cycle: P : in out 1 – i rises during tick i – i falls during tick ((i+1) mod 4)+1 P 1 2 3 4 Tick # 1 2 3 4 P 2LAL Cycle of Operation in1 in 21 in0 20 out1 11 in=0 11 10 21 out0 out=0 10 Shift Register Structure • 1-tick delay per logic stage: 2 3 4 1 in out 1 2 3 4 • Logic pulse timing & propagation: 1 2 3 4 ... in in 1 2 3 4 ... More complex logic functions • Non-inverting Boolean functions: A B A A B AB AB • For inverting functions, must use quad-rail A=0 A=1 logic encoding: A0 A0 • Zero-transistor A1 A1 “inverters.” – To invert, just swap the rails! 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 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.