IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015

619

Asynchronous Domino Logic Pipeline Design
Based on Constructed Critical Data Path
Zhengfan Xia, Masanori Hariyama, and Michitaka Kameyama
Abstract— This paper presents a high-throughput andultralow-power asynchronous domino logic pipeline design
method, targeting to latch-free and extremely fine-grain orgate-level design. The data paths are composed of a mixtureof dual-rail and single-rail domino gates. Dual-rail domino gatesare limited to construct a stable critical data path. Based on thiscritical data path, the handshake circuits are greatly simplified,
which offers the pipeline high throughput as well as low power
consumption. Moreover, the stable critical data path enables the
adoption of single-rail domino gates in the noncritical data paths.
This further saves a lot of power by reducing the overheadof logic circuits. An 8 × 8 array style multiplier is used forevaluating the proposed pipeline method. Compared with abundled-data asynchronous domino logic pipeline, the proposed
pipeline, respectively, saves up to 60.2% and 24.5% of energy inthe best case and the worst case when processing different data
patterns.
Index Terms— Asynchronous pipeline, critical data path,dual-rail domino gate, single-rail domino gate.

D

I. I NTRODUCTION

URING the last decade, there has been a revival inresearch on asynchronous technology. Along with thecontinued CMOS technology scaling, VLSI systems become
more and more complex. The physical design issues, such as
global clock tree synthesis and top-level timing optimization,
become serious problems. Even if technology scaling offers
more integration possibilities, modularity and scalability are
difficult to be realized at the physical level. Asynchronous
design is considered as a promising solution for dealing withthese issues that relate to the global clock, because it uses local
handshake instead of externally supplied global clock [1]–[4].
The attractive properties are listed as follows:
1) low power consumption;

Manuscript received September 5, 2013; revised February 17, 2014;
accepted March 25, 2014. Date of publication April 18, 2014; date of current
version March 18, 2015. This work was supported in part by the Ministry of
Education, Culture, Sports, Science and Technology KAKENHI under Grant
12020735, in part by the Ministry of Economy, Trade and Industry, through the
Research and Development Subsidiary Program for Promotion of Academiaindustry Cooperation, in part by VLSI Design and Education Center, andin part by the University of Tokyo through STARC, e-Shuttle Inc., FujitsuLtd., Cadence Design Systems Inc., Synopsys Inc., and Mentor Graphics
Inc. This paper was presented at the dual-rail/single-rail hybrid logic designconcept appeared in the 2012 IEEE International Symposium on Circuits
and Systems, May 2012, pp. 3017–3020, as dual-rail/single-rail hybrid logic
design for high-performance asynchronous circuit and the construction of thecritical data path using synchronizing logic gates appeared in the 2012 IEICE
Transaction on Electronics, Vol. E95-C, no. 8, pp. 1434–1443, Aug. 2012, as
design of high-performance asynchronous pipeline using synchronizing logic
gates.
The authors are with the Graduate School of Information Sciences, Tohoku
University, Sendai 980-8579, Japan (e-mail: xiazhengfan@ecei.tohoku.ac.jp;
hariyama@ecei.tohoku.ac.jp; kameyama@ecei.tohoku.ac.jp).
Digital Object Identifier 10.1109/TVLSI.2014.2314685

2) high operating speed;3) no clock distribution and clock skew problems;4) better composability and modularity;5) less emission of electromagnetic noise;6) robustness toward variations in supply voltage, temperature, and fabrication process parameters.
In asynchronous design, the choice of handshake protocols affects the circuit implementation (area, speed, power,
robustness, etc.). The four-phase bundled-data protocol andthe four-phase dual-rail protocol are two popular protocols
that are used in most practical asynchronous circuits. The fourphase bundled-data protocol design most closely resembles thedesign of synchronous circuits. Handshake circuits generate
local clock pulses and use delay matching to indicate valid
signal. It normally leads to the most efficient circuits due tothe extensive use of timing assumptions. On the other hand,the four-phase dual-rail protocol design is implemented in an
elaborate way that the handshake signal is combined with thedual-rail encoding of data. Handshake circuits are aware of thearrival of valid data by detecting the encoded handshake signal,
which allows correct operation in the presence of arbitrary
data path delays. This feature is very useful for dealing withdata path delay variations in advanced VLSI systems, such as
asynchronous field-programmable gate arrays (FPGAs) [5]–[7]and system-on-chip [3], [4]. However, such attractive featureis realized at the expense of encoding and detection overheads.
These overheads cause low circuit efficiency and restrict theapplication area of the four-phase dual-rail protocol design.
This paper presents a novel design method of asynchronous
domino logic pipeline, which focuses on improving the circuit
efficiency and making asynchronous domino logic pipeline
design more practical for a wide range of applications. The
novel design method combines the benefits of the four-phasedual-rail protocol and the four-phase bundled-data protocol,
which achieves an area-efficient and ultralow-power asynchronous domino logic pipeline.
Asynchronous domino logic pipeline is an interesting
pipeline style that can entirely avoid explicit storage elements
between stages by exploiting the implicit latching functionalityof domino logic gates. The latchless feature provides thebenefits of reduced critical delays, smaller silicon area, andlower power consumption.
However, asynchronous domino logic pipeline has a common problem that dual-rail domino logic has to be used
to compose the domino data path. Single-rail domino logic
cannot be used because it would break the domino data pathsince only noninverting logic can be implemented [13]. As a1063-8210 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

620

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015

result, the domino data path has a dual-rail encoding overheadthat consumes a lot of silicon area and power consumption.
Such overhead almost cancels out the area and power benefits
provided by the latchless feature.
Another problem is the overhead of handshake control logic.
Conventional designs of asynchronous domino logic pipeline
based on the four-phase dual-rail protocol rely on domino data
path to transfer data and encoded handshake signal, and use
completion detectors to detect and collect the handshake signal
throughout the entire data paths [8]–[11]. Such design method
is very robust for delay variations in data paths. However, itcauses a serious detection overhead. The detection overhead
is growing with the width of data paths, which impedes its
application in the design of a large function block with aconsiderable data path width. On the other hand, asynchronous
domino logic pipeline based on the four-phase bundled-data
protocol avoids the detection overhead by implementing asingle extra bundling signal, to match the worst case blockdelay, which serves as a completion signal. The problem is that
this design method completely loses the good properties in thefour-phase dual-rail protocol design. Besides, it does not solve
the dual-rail encoding overhead problem in data paths [12].
In this paper, our proposed pipeline reduces both thedual-rail encoding overhead in data paths and the detection
overhead in handshake control logic by designing basedon a constructed critical data path. A stable critical data
path is constructed using redesigned dual-rail domino gates.
By detecting the stable critical data path, a 1-bit completion
detector is enough to get the correct handshake signal regardless of the data path width. Such design does not only greatly
reduce the detection overhead but also partially maintains thegood properties in the four-phase dual-rail protocol design.
Moreover, the stable critical data path serves as a matching
delay to solve the dual-rail encoding overhead problem in data
paths. With the help of the redesigned dual-rail domino gates,
single-rail domino logic is successfully applied in noncritical
data paths. As a result, the proposed asynchronous domino
logic pipeline has a small overhead in both handshake control
logic and function block logic, which greatly improves thecircuit efficiency. According to the design feature, we namethe proposed pipeline as asynchronous pipeline based on
constructed critical data path (APCDP).
This paper is organized as follows. Section II introduces
the background of asynchronous domino logic pipeline. PS0
is introduced to demonstrate the advantages and problemsof asynchronous domino logic pipeline based on dual-rail
protocol. Several related designs are also simply introduced.
Section III focuses on the introduction of the proposed pipeline
design method. Synchronizing logic gates (SLGs) and synchronizing logic gates with a latch function (SLGLs) are introduced to construct a stable critical data path. The robustness ofthe pipeline structure and the constructed critical data path isanalyzed. Then, more complex pipeline structures are further
discussed. Section IV presents the evaluation results that show
the benefits of the proposed pipeline compared with a bundleddata asynchronous domino logic pipeline and a synchronous
pipeline with a sequential clock gating (Sync-CG). Section V
presents the conclusion.

TABLE IC ODE TABLE OF THE F OUR -P HASE D UAL -R AIL E NCODING

Fig. 1.

Block diagram of PS0.

II. BACKGROUND
PS0 is a well-known implementation style of asynchronous
domino logic pipeline based on dual-rail protocol [8]. It is
an important foundation for most later proposed styles. Since
our proposed pipeline is also based on PS0, we will begin byreviewing PS0 pipeline style, and then simply introducing twoother advanced styles: 1) a timing-robust style called precharge
half-buffer [9] and 2) a high-throughput style called lookahead
pipeline [11]. Finally, we summary the delay assumptions ofthese pipelines and give our delay assumption in the proposed
design.
A. PS01) Four-Phase Dual-Rail Protocol: PS0 is designed basedon the four-phase dual-rail protocol. Fig. 3 shows an example
of data transfer based on the four-phase dual-rail protocol,
and Table I shows the code table of the four-phase dual-rail
encoding. The four-phase dual-rail encoding encodes a request
signal into the data signal using two wires, (w_t, w_ f ). The
data value 0 is encoded as (0, 1), and value 1 is encoded as(1, 0); the spacer is encoded as (0, 0); (1, 1) is not used. Whentransferring the valid data, a spacer is inserted between them.
A receiver can easily obtain the valid data by monitoring thetwo wires. This protocol is very robust since a sender and a
receiver can communicate reliably regardless of delays in the
combinational logic block and wires between them. The dualrail encoded data path is known as the delay-insensitive data
path.
2) Structure of PS0: Fig. 1 shows a block diagram of PS0.
In PS0, each pipeline stage is composed of a function blockand a completion detector. Each function block is implemented
using dual-rail domino logic. Each completion detector generates a local handshake signal to control the flow of data
through the pipeline. The handshake signal is transferred toXIA et al.: ASYNCHRONOUS DOMINO LOGIC PIPELINE DESIGN

621

Fig. 2.

(a) Dual-rail domino AND gate. (b) Two-bit completion detector.

Fig. 3.

Example of data transfer based on four-phase dual-rail protocol.

the precharge/evaluation control port of the previous pipeline
stage.
Fig. 2 shows an example of the dual-rail domino AND gate
and the 2-bit completion detector. A two-input NOR gate serves
as the 1-bit completion detector to generate a bit done signal
by monitoring the outputs of dual-rail domino gate. To builda 2-bit completion detector, C-element is needed to combine
the bit done signals. A full completion detector is formed by
combining all bit done signals from the entire data paths witha tree of C-elements, as shown in Fig. 1.
3) Protocol of PS0: The protocol of PS0 is quite simple.
F(N) is precharged when F(N + 1) finishes evaluation. F(N)evaluates when F(N + 1) finishes its reset, or precharge.
In Fig. 1, if we observe a single data flow through an initiallyempty pipeline in which every pipeline stage is in evaluation
phase, the complete cycle of events is as follows.
1) F1 evaluates and data flow to F2.
2) F2 evaluates and data flow to F3. F2’s completion
detector detects completion of evaluation and sends aprecharge signal to F1.
3) F1 precharges and F3 evaluates. F3’s completion detector detects completion of evaluation and sends aprecharge signal to F2.
4) F2 precharges. F2’s completion detector detects thecompletion of precharge and sends an evaluation signal(enable signal) to F1. The evaluation signal enables F1
to evaluate new data once again.
There are three evaluations, two completion detections, andone precharge in the complete cycle for a pipeline stage. The
pipeline cycle time Tcycle isTcycle = 3tEval + 2tCD + tPrech(1)where tEval and tPrech are the evaluation and precharge times
for each stage and tCD is the delay through each completion
detector.
4) Overhead Problems: There are mainly two overhead
problems that prohibit the widespread use of PS0, the detection
overhead in handshake control logic and the dual-rail encoding
overhead in function block logic. A ripple carry adder, shown

Fig. 4.

Pipelined 4-bit ripple carry adder.

Fig. 5.

Block diagram of PCHB.

in Fig. 4, is used as an example to clarify these overhead
problems.
The detection overhead is caused by the full completion
detectors that are used to deal with data path delay variations
by detecting the entire data paths. The overhead greatly affects
the pipeline speed and power consumption. The most serious
problem is that the detection overhead is growing the widthof data paths. In a 4-bit ripple carry adder, the width of data
paths is between 8 and 5 bits. The detection overheads of
8–5-bit completion detectors might be acceptable in practicaldesign. However, in 32-bit ripple carry adder design, the widthof data paths is at least 33 bits. The overhead of 33-bit
completion detector is so large that PS0 is hardly applicablein such situation. Even the detection time can be reduced bypartitioning wide data path into several data streams [11], thedetection power is not reduced.
The dual-rail encoding overhead is caused by dual-rail
domino logic that is used for not only implementing logic
function but also storing data between pipeline stages. Because
there are no explicit storage elements (latches or registers),
a lot of dual-rail domino buffers have to be added to levelize
each stage. The added dual-rail domino buffers consume alot of silicon area and power. In a 4-bit ripple carry adder,
18 dual-rail domino buffer gates are added, which almost
cancel out the benefit of removing explicit storage elements.
B. Other Advanced Pipelines
1) Precharge Half-Buffer Pipeline: Fig. 5 shows a block
diagram of precharge half-buffer pipeline (PCHB). PCHB is atiming-robust pipeline style that uses quasi-delay-insensitive
control circuits [9]. Two completion detectors in a PCHB
stage: one on the input side (Di ) and one on the output
side (Do ). The complete cycle of events for a PCHB stage isquite similar to that of PS0, except that a PCHB stage verifies
its input bits. Because of the input completion detector (Di ),a PCHB stage does not start evaluation until all input bits arevalid. This design absorbs skew across individual bits in the622IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015

Fig. 7.

Fig. 6. Block diagrams of LP2/2. (a) LP2/2 based on dual-rail protocol.
(b) LP2/2-SR.

data paths. Although this design makes PCHB more timing
robust, it causes a two-time overhead in handshake control
logic compared with PS0. Besides, PCHB has the same dualrail encoding overhead as PS0.
2) LP2/2: LP2/2 is a high-throughput pipeline style [11],which has both dual-rail protocol design and bundled-data
protocol design.
Fig. 6(a) shows the block diagram of LP2/2 based on the
dual-rail protocol. LP2/2 improves the throughput of PS0 by
optimizing the sequential of handshake events. However, they
do not solve the overhead problems in handshake control logic
and function block logic. The handshake speed is accelerated
by employing asymmetric completion detectors placed aheadof function blocks. Although this pipeline structure reduces
the handshake cycle time, the asymmetric completion detectors
still consume a lot of power since they have to detect the entire
data paths.
Fig. 6(b) shows the block diagram of LP2/2 based on
the bundled-data protocol (LP2/2-SR). LP2/2-SR avoids thedetection overhead problem by implementing a single extra
bundling signal. The bundling signal serves as a completion
signal, which matches the worst case delay in function blocks.
Although such design reduces the power consumption inhandshake control logic, the overhead problem in function
block logic remains unsolved since dual-rail domino logic still
has to be used to compose the domino data path [12].
C. Delay Assumptions
PCHB is a very robust pipeline that requires no delay
assumptions or calculations by designer. However, the robustness of circuits comes at the expense of performance. The
complex handshake circuits slow down the handshake speed
and consume more power.
PS0 is designed for fast handshake speed by seeking todesign control circuits that are always correct for common
conditions. It is based on a delay assumption that each pipeline

Block diagram of APCDP.

stage’s predecessor precharges no slower than the stage’s
successor evaluates.
Based on PS0, LP2/2 makes two more aggressive delay
assumptions: first, each pipeline stage evaluates no slower thanits completion detects plus the stage’s successor precharges.
Second, each pipeline stage completion detects plus its predecessor precharges no slower than the stage evaluates plus its
successor completion detects. Although these delay assumptions improve the pipeline throughput, they sacrifice thepipeline robustness.
Our proposed pipeline is based on PS0, but makes adifferent delay assumption from LP2/2. We assume that, inthe evaluation of domino gates, a n-stack pull-down pathcauses larger delay than a m-stack pull-down path (n is larger
than m). Based on this delay assumption, we construct a stable
critical data path for improving the circuit efficiency in both
handshake control logic and function block logic. Because this
delay assumption is made on gate level instead of handshakestructure level, our proposed pipeline has, structurally, thesame robustness as PS0.
III. A SYNCHRONOUS P IPELINE BASED ON
C ONSTRUCTED C RITICAL DATA PATH
A. Overview
Fig. 7 shows the block diagram of the proposed asynchronous pipeline (APCDP). The pipeline is designed based on astable critical data path that is constructed using a special dualrail logic. The critical data path transfers a data signal and an
encoded handshake signal. Noncritical data paths, composedof single-rail logic, only transfer data signal. A static NOR
gate detects the dual-rail critical data path and generates a
total done signal for each pipeline stage. The outputs of NOR
gates are connected to the precharge ports of their previous
stages.
APCDP has the same protocol as PS0. The differenceis that a total done signal is generated by detecting only
the critical data path instead of the entire data paths. Suchdesign method has two merits. First, the completion detector
is simplified to a single NOR gate, and the detection overhead
is not growing with the data path width. Second, the overheadof function block logic is reduced by applying single-rail
logic in noncritical data paths. As a result, APDCP has asmall overhead in both handshake control logic and function
block logic, which greatly improves the throughput and power
consumption.
APCDP is more familiar to bundled-data asynchronous
pipeline because the critical data path essentially works as

XIA et al.: ASYNCHRONOUS DOMINO LOGIC PIPELINE DESIGN

623

TABLE IIS TATES OF P ULL -D OWN T RANSISTOR PATHS
ON D IFFERENT D ATA PATTERNS

Fig. 8.

a matching delay, which controls the correct data transfer innoncritical data paths. Compared with conventional bundleddata design using a separate matching delay to match theworst case delay in function blocks, the proposed design
method reuses the existing function block logic to provide thematching delay. Such design has many advantages. First, thematching delay is accurate. The matching delay in APCDP isexactly the same worst case delay in function blocks. Second,
the matching delay is robust for delay variations. Dual-rail
critical data path supplies delay-insensitive property, which canbe self-adaptive to delay variations in function blocks. Third,
the handshake control logic is efficient in area and power. The
handshake control logic is implemented by reusing the existing
function block logic.
Finding a stable critical data path in function blocks isvery important in the proposed design. The problem is that
it is difficult to get a stable critical data path using traditional
logic gates. Traditional logic gates have the gate-delay datadependence problem—the gate delay is dependent on input
data patterns. For example, the ripple carry adder in Fig. 4.
The ripple carry path seems to be the stable critical data path.
However, actually, the critical data path varies according todifferent input data patterns. Because of the gate-delay datadependence problem, the carry function gate can be triggered
early by the input bits (an and bn ) regardless of the carry bit.
Since the input bit travels faster in the buffer path than the
carry bit in the ripple carry path, it cannot guarantee that thecritical transition signal always presents on the ripple carrypath.
Adding delay elements is an intuitive way to construct astable critical data path. However, this method needs complex
timing analysis and would cause huge overhead of delay
elements. This paper introduces an efficient solution that uses
SLGs to construct the critical data path. The SLGs solve
the gate-delay data-dependence problem by making sure that
SLGs cannot start evaluation until all valid data arrive [14].
This feature does not only help to construct a stable critical
data path but also enable the adoption of single-rail domino
logic in the noncritical data paths. As a result, the proposed
design is significantly area and power efficient.
B. Logic Gates
In VLSI circuits, it is difficult to get a stable critical data
path using traditional logic gates due to the gate-delay datadependence problem. Fig. 2(a) shows a traditional dual-rail
domino AND gate. The true side of logic is implemented
by out_t = a_t · b_t and the false side by out_ f =Synchronizing AND gate and the truth table of dual-rail AND logic.

Fig. 9. Synchronizing AND gate with a latch function and the table of latch
states.

a_ f +b_ f . Table II shows the states of pull-down transistor
paths on different data patterns. In traditional dual-rail domino
AND gate, there are three transistor paths: 1) [a_t, b_t];2) [a_ f ]; and 3) [b_ f ]. First of all, these paths have different
number of transistors at the sequential position. When theyturn ON, respectively, [a_ f ] and [b_ f ] cause less delays than[a_t, b_t]. Moreover, when the data pattern is (0, 1, 0, 1),[a_ f ] and [b_ f ] will be both ON, which leads to a muchquicker signal transfer. As a result, the gate delay has alarge variation depending on different data patterns. To solve
the gate-delay data-dependence problem, SLG and SLGL are
introduced [14].
1) Synchronizing Logic Gates: SLGs are dual-rail domino
gates that have no gate-delay data-dependence problem. Fig. 8
shows the synchronizing AND gate and the truth table of dualrail AND logic. The principle is that, in the pull-down network,
there is exactly one path activated according to one data
pattern, and the stack of all possible paths is kept constant at
the sequential position. Compared with the traditional design,
the false side logic expression is changed to out_ f = a_t ·b_ f + a_ f · (b_t + b_ f ). Table II shows that there are fourtransistor paths: 1) [a_t, b_t]; 2) [a_t, b_ f ]; 3) [a_ f, b_t]; and[a_ f, b_ f ]. Every path has two transistors at the sequential
position, and there is only one path turns ON corresponding
to an input data pattern. As a result, the gate delay becomes
independent on different data patterns. This kind of gates isnamed as SLGs because they can synchronize their inputs.
The SLGs verify that all data signal transitions have arrived
on their inputs before changing their outputs.
The characteristics of SLGs are listed as follows.
1) An SLG has a certain number, inputs’ number, oftransistors in pull-down transistor paths at the sequential
position.

624

Fig. 10.

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015

Structure of APCDP.

2) An SLG has no gate-delay data-dependence problem.
Its gate delay mainly relates to the inputs number.
3) An SLG can synchronize its inputs. The SLG cannot
start evaluation until all valid data arrive.
2) Synchronizing Logic Gates With a Latch Function: Basedon the characteristics of SLGs, SLGLs are extended. Fig. 9shows synchronizing AND gate with a latch function and thetable of latch states. An SLGL has an enable port (en_t, en_ f ),which controls the opaque and transparent state of the SLGL.
The principle is that SLGLs cannot start evaluation without
the presence of the enable signal.
Same as the dual-rail AND logic, all traditional dual-rail
domino logic can be redesigned to become an SLG or an
SLGL. The critical data path in dual-rail asynchronous pipeline
can be easily constructed using SLGs and SLGLs.
C. Structure of APCDP
Fig. 10 shows the structure of APCDP. The solid arrow
represents a constructed critical data path (dual-rail data path),the dotted arrow represents the noncritical data paths (singlerail data paths), and the dashed arrow represents the output of
single-rail to dual-rail encoding converter.
In each pipeline stage, a static NOR gate is used as
1-bit completion detector to generate a total done signal forthe entire data paths by detecting the constructed critical
data path. Driving buffers deliver each total done signal tothe precharge/evaluation control port of the previous stage.
Since the completion detector only detects the constructed
critical data path, the noncritical data paths do not have totransfer encoded handshake signal anymore. Therefore, singlerail domino gates are used in the noncritical data path tosave logic overhead. Encoding converter is used to bridge
the connection between single-rail domino gate and dual-rail
domino gate.
1) Construction of the Critical Data Path: It is difficult toconstruct a stable critical data path using traditional logic gates
for their gate-delay data-dependence problem. The criticalsignal transition varies from one data path to others according
to different input data patterns. Since SLGs have solved thegate-delay data-dependence problem, a stable critical data pathcan be easily constructed by the following steps:

1) finding a gate (named as Lin gate) that has the largest
number of inputs in each pipeline stage;2) changing these Lin gates to SLGs;
3) linking SLGs together to form a stable critical data path.
The basic idea of finding the critical signal transition is thatembedding an SLG in each pipeline stage and making the SLG
to be the last gate to start and finish evaluation. First of all, theembedded SLG has the largest gate delay in a pipeline stage.
The reasons are as follows.
1) The SLG has the largest stack in the pull-down network
compared with other gates.
2) The SLG has only one pull-down transistor path activated for each input data pattern.
Then, if all gates evaluate at the same time or the SLG is thelast gate to start evaluation in the pipeline stage, the criticalsignal transition would present on the output of the SLG.
In practice, making all gates evaluate at the same time isdifficult, especially without the help of intermediate latches orregisters. Therefore, we make the SLG become the last gate tostart evaluation by linking each pipeline stage’s SLG together.
In the first pipeline stage, the critical signal transition is on
the output of the SLG because all gates evaluate at the sametime for the input control of latches or registers. After linking
each pipeline stage’s SLG together, the SLG in the following
pipeline stage would be the last gate to start evaluation since italways waits for the critical signal transition from the previous
SLG. As a result, the linked SLG data path becomes a stable
critical data path.
Linking each pipeline stage’s SLG together is partially donein the process of selecting Lin gate in each pipeline stage.
When searching Lin gate, there might be more than one option.
It is best to select the Lin gate that is originally linked to the
Lin gate in the following pipeline stage. After changing these
Lin gates to SLGs, SLGs are naturally linked. For example,
the linkage between Stage1 and Stage2 in Fig. 10. However, if
we cannot find the linked Lin gates in neighbor stages, SLGL
needs to be used to solve the linking problem. The linkage
between Stage2 and Stage3 is in such situation. The linkage
is established by connecting the output of SLG in Stage2 andthe enable port of SLGL in Stage3.

XIA et al.: ASYNCHRONOUS DOMINO LOGIC PIPELINE DESIGN

Fig. 11.

Encoding converters. (a) Intuitive design. (b) Proposed design.
TABLE IIIT RUTH TABLE OF E NCODING C ONVERTER

625

conversion speed of the encoding converter. Interestingly, we
do not have to care about the conversion from the singlerail data0 in = 0 to the dual-rail data0 (out, out) = (0, 1).
Because the converter initially outputs a dual-rail data0, thisconversion can be considered infinite fast. We only have tofocus on improving the conversion from the single-rail data1
in = 1 to the dual-rail data1 (out, out) = (1, 0). Fig. 11(b)shows the proposed design of the encoding converter. Whenthe converter enters the evaluation phase, the input in = 1 canimmediately pull down out. No matter the output (out, out) is
a instant spacer (0, 0) or the valid data1 (1, 0), it effectively
protects the data transfer error. On the other hand, the intuitive
design in Fig. 11(a) has a longer signal transition delay. out
cannot be pulled down until out becomes 1. It has a higher
possibility of causing data transfer error than the proposed
encoding converter.
D. Robustness Analysis

2) Encoding Conversion: Since the completion detector
detects only the constructed critical data path, the noncritical
data paths do not have to transfer encoded handshake signal
anymore. The logic overhead in the noncritical data paths canbe reduced using single-rail domino gates instead of dual-rail
domino gates. However, single-rail domino gate and dual-rail
domino gate use different encoding schemes. It has encoding
compatibility problem when a single-rail domino gate connects
to a dual-rail domino gate. Encoding converter needs to be
designed to solve the problem.
Fig. 11 shows two implementations of encoding converter.
Table III shows the truth table. In precharge phase pc = 0,
encoding converter outputs a dual-rail data0 (out, out) = (0, 1).
In evaluation phase pc = 1, if the input is a single-rail data0
in = 0, the converter keeps the dual-rail data0. If the input is asingle-rail data1 in = 1, the converter outputs a dual-rail data1(out, out) = (1, 0). Since single-rail encoding only has twostates that, respectively, represent data0 and data1, there is noother state that can be converted to spacer (out, out) = (0, 0).
The disappearance of spacer violates the four-phase dual-rail
protocol, which would cause data transfer error.
Fig. 10 shows two examples that encoding converters areused to bridge the connection between single-rail domino gate
and dual-rail domino gate. Focusing on the encoding converterin Stage2, when Stage2 enters the precharge phase, the SLG
outputs a spacer, but the converter outputs a invalid data0.
This invalid data0 cannot be absorbed by the SLGL in Stage3
since the spacer impedes its evaluation. However, when Stage2
enters the evaluation phase, it has a risk that the invalid
data0 might be erroneously absorbed if the output of the SLG
becomes valid earlier than the output of the converter. The
earlier arrived valid data from the SLG trigger the SLGL tostart evaluation and absorb the invalid data0. To avoid thisproblem, the encoding converter needs to satisfy a timing
constraint that the output of the converter should become valid
earlier than the output of SLG. In other words, the constructed
critical data path should be robust.
In addition to protect data transfer error by enhancing therobustness of the critical data path, we can also improve the

APCDP has pipeline failure in the situation that a pipeline
stage does not finish evaluating before its previous stage startprecharge. In such situation, the pipeline stage cannot correctly
finish evaluating because the precharge of its previous pipeline
stage removes the valid data from the inputs. To avoid thispipeline failure, APCDP needs to satisfy an assumption that,in a pipeline stage, none of the other bits across the entire
data paths is slower than the detected bit by more than the
delay through a static NOR gate and the drive buffer chain
following it. The robustness of APCDP is analyzed based on
this assumption.
1) Robustness of the Pipeline Structure: According to thepipeline structure of APCDP, the hold time Thold of valid dataon the inputs of each pipeline stage is
Thold = tSLG_Eval + tNOR + tBuf + tSLG_Prech(2)

where tSLG_Eval is the evaluation time for the SLG in a pipeline
stage and tSLG_Prech is the precharge time for the SLG in theprevious pipeline stage. tNOR + tBuf is the delay through the
NOR gate and the drive buffer.
The pipeline structure of APCDP is quite robust since
the hold time Thold supplies sufficient time margins. In theconstruction of the critical data path, we introduced that the
SLG is embedded as the last gate to finish evaluation in eachpipeline stage. There are even some gates that are slower
than the SLG because of delay variations in practice, Tholdsupplies tNOR + tBuf + tSLG_Prech time margins for pipeline
failure protection. We believe that these time margins are
sufficient for dealing with delay variations in practical design.
However, for safety, we supply several enhance measurements
for the constructed critical data path in the following section.
2) Robustness of the Critical Data Path: We first use themethod of logical effort [19] to analyze the robustness of theconstructed critical data path. Then, we discuss how to further
enhance the robustness of the constructed critical path.
The method of logical effort is an easy way to estimate delay
in CMOS circuit. In the method, modeling delay of a logic
gate isolates the effects of a particular fabrication process byexpressing all delays in terms of a basic delay unit particular to626IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015that process. The delay incurred by a logic gate is comprised of
two components: 1) a fixed part called the parasitic delay p
and 2) a part that is proportional to the load on the gate’s
output, called the effort delay f . This effort delay depends
on the load and the properties of the logic gate driving theload. There are two related terms for these effects: the logicaleffort g captures the effect of the logic gate’s topology on its
ability to produce output current, while the electrical effort
h describes how the electrical environment of the logic gateaffects performance and how the size of the transistors in thegate determines its load-driving capability. Electronic effort isalso called fanout by many CMOS designer. As a result, thedelay of a logic gate is expressed as
Cout
+p
(3)
Cin
where Cout is the capacitance that loads the output of the logic
gate and Cin is the capacitance presented by the input terminalof the logic gate.
In each pipeline stage of APCDP, the SLG/SLGL has alarger gate delay than other gates according to the methodof logic effort. First, the SLG/SLGL has more complicatedtopology than other gates in the pull-down network. It slightly
increases the parasitic delay p and the logical effect g. Second,the output of SLG/SLGL is connected to a static NOR gate andthe SLG/SLGL in the next stage. Compared with the outputsof other gates, the SLG/SLGL has a larger fanout Cout , which
increases the electrical effort h. As a result, the SLG/SLGL
has a larger gate delay than traditional logic gates even they
have same number of inputs. When linking all SLGs/SLGLs
together, these imposed delays increase the robustness of theconstructed critical data path.
In practice, the robustness of the constructed critical path isaffected by delay variations. As a matter of fact, it is a common
problem in VLSI circuit design, same as the robustness of aclock signal in synchronous design and a match delay line inbundled-data asynchronous design [2]. As we all know, these
designs all suffer from delay variations. To resist the influenceof delay variations, synchronous design enlarges the cycle timeof a clock signal to get some margin. On the other hand,bundled-data asynchronous design adds extra delay margin
on the matching delay line to match the worst case delay in
combinational logic block. Same like these solutions, the delay
variations problem in the proposed design can be solved byenlarging delay margin on the constructed critical data path.
We supply four measures to enlarge the delay margin, which
are listed as follows:
1) sizing the pull-down transistors or the static inverters of
SLGs and SLGLs to increase gate delays;
2) applying a low priority in circuit layout for the constructed critical path;3) improving the noncritical paths delay;4) adding delay elements on the critical path.
These measures have different impacts on the performanceof circuits. It is better to choose a proper measure or multiple measures according to the practical design requirements.
In measure 1), reducing the transistor size of pull-down
network or the static inverters can increase the gate delays
delay = f + p = gh + p = g

Fig. 12.

(a) Fork structure. (b) Join structure.

of SLGs and SLGLs. The increased delay slightly slows
down pipeline speed, but smaller transistor size helps insaving power and silicon area. Measure 2) is layout optimization. Although this measure slightly decreases pipeline
speed, it does not impose the extra overhead of transistors.
Measure 3) does not degrade pipeline speed. The problem isthat improving the noncritical path delay would increase thepower consumption. Measure 4) is an intuitive way to enhance
the critical data path. The drawback is the extra overhead oftransistors.
In addition, the use of domino logic introduces many designrisks because it is very sensitive to noise, circuit, and layout
topologies [20]. The solutions to alleviate these problems are
not in the scope of this paper. We only recommend to limit
the largest stack of domino logic when designing APCDP.
The limitation depends on processing technology, practicalproblems, and actual conditions. Smaller stack design helps
in alleviating the noise problems and increasing the pipeline
speed. The tradeoff is the increased number of pipeline stages.
More pipeline stages means larger silicon area and higher
power consumption. On the other hand, larger stack design
deteriorates the noise problems and the pipeline speed. The
merit is the reduced number of pipeline stages. Less pipeline
stages helps in saving silicon area and power consumption.
E. Extension to Complex Structures
The previous sections just analyzed the linear pipeline
structure. For more complex data paths, forks and joins areneeded [2]. Fig. 12 shows fork structure and join structure in
APCDP.
In fork structure, the outputs of function block A are split
to connect with function blocks B and C. C-element is used
to collect the handshake signal from A’s successors. The

XIA et al.: ASYNCHRONOUS DOMINO LOGIC PIPELINE DESIGN

627

construction of the critical data path in fork structure is sameas that of described in the linear structure. The problem isthat the data paths from A to B and C are more complex
than the linear structure. The complex data paths cause large
delay variations, which affect the correctness of the critical
data paths at the inputs of B and C. Pipeline failure happens
when B and C do not finish their evaluations before A finishes
its precharge. The delivery time of the precharge signal from
B and C to A is that
Tdel = TNOR + TC + Tbuffer

TABLE IVE VALUATION R ESULTS OF 8×8 A RRAY S TYLE M ULTIPLIERS(4)

where TNOR , TC , and Tbuffer are delay time of a static NORgate, a C-element, and the buffer gate. If the delay variations
on the data paths are smaller than Tdel , no pipeline failure
happens.
In join structure, the outputs of function block A and B
merge together at function block C, which requires sending an
acknowledge signal from C to all its predecessors. In function
block C, the critical data paths from function block A and B
need to simultaneously connect to an SLG/SLGL. The design
process is similar to that of described in the linear structure.
The problem in join structure is that the acknowledge signal
networks at function block B and C are more complex thanthe linear structure. Pipeline failure happens when A and B
do not completely finish their precharge process before C
enters the next evaluation phase, which means that C would
mistakenly absorb old data from A or B. The delivery time ofthe precharge signal from C to A and B is that
Tdel = TNOR + Tbuffer .

(5)

According to the handshake protocol, the time for C to enter
the next evaluation phase is thatTnextEval = 2TEval + 2TNOR + 2Tbuffer(6)

where TEval is the evaluation time for a function block.
Therefore, the margin time is that
Tmargin = TnextEval − Tdel = 2TEval + TNOR + Tbuffer .

(7)

If the delay variations on the acknowledge signal networks are
smaller than Tmargin , no pipeline failure happens.
IV. E VALUATIONThis section presents the evaluation results of APCDP.
An 8 × 8 array style multiplier is chosen as the test case,which is, respectively, designed using the proposed APCDP,
LP2/2-SR [11], classic synchronous pipeline (Sync), and SyncCG [15], [16]. Conventional dual-rail asynchronous pipelines
are not selected as the evaluation counterparts because they are
hardly applicable in the design of large function block (suchas the 8 × 8 array style multiplier).
A. Experiment Setup
Four 8 × 8 array style multipliers are designed using
HSPICE in a 65-nm design technology. All designs are simulated at 1.2 V normal supply voltage, 85 °C temperature, anda normal process corner.

Fig. 13. Energy consumption per cycle for processing different data patterns.

LP2/2-SR is chosen as a representative of latchlesspipeline for comparing with APCDP. LP2/2-SR was proposed along with LP2/2, which is significantly morearea and energy efficient. It was reported that LP2/2SR had about 60% smaller area and 55% lower energy
consumption than LP2/2 in first-input first-output (FIFO)
design [11]. Besides, LP2/2-SR resembles the design of latchless synchronous pipeline. The difference is that latchlesssynchronous pipeline uses a complex multiphase clocking
instead of bundled-data handshaking. Because of their similarity, the performance of LP2/2-SR can be used as a reference
for comparing APCDP with latchless synchronous pipeline.
An 8 × 8 array style multiplier is extremely fine-grain orgate-level pipelined using LP2/2-SR as well as APCDP. The
depth of each pipeline stage is only one domino logic gate, andthere are no explicit storage elements between stages. Their
comparisons show not only the circuit efficiency of APCDP
but also the merits of dual-rail asynchronous design.
To make a further comparison, Sync and Sync-CG are also
designed. They are used as comparison references since they
do not belong to latchless pipeline. The 8 × 8 array stylemultiplier is divided into five pipeline stages. The logic blocks
are composed of static logic gates, and D flip-flops are used
as intermediate storage elements between pipeline stages. The
sequential clock gating in Sync-CG is designed using six D
flip-flops, which realizes fine-grain clock gating that is similar
to the handshake behaviors in APCDP and LP2/2-SR.

628

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015

Fig. 14. Performances of power consumption (all designs operate at 3.6G
dataset/s).

B. Results
Table IV shows the evaluation results of the 8 × 8 arraystyle multiplier. The performances of throughput are evaluated
without considering design margins, which are ideal results.
The results show that APCDP has high throughput, the smallest transistor count, and the lowest forward latency in all
designs. Fig. 13 shows the energy consumption for processing
different data patterns. Fig. 14 shows the performances ofpower consumption under different workloads. The results
show that APCDP is the most power efficient design.
1) Transistor Count: Table IV shows that APCDP,
respectively, reduces the transistor count by 25.3% and 18.1%
compared with LP2/2-SR and Sync. APCDP uses a mixtureof dual-rail domino logic and single-rail domino logic. The
single-rail domino logic gates in the noncritical data paths
save a lot of the transistor count. Although the SLGs and
SLGLs in APCDP consume more transistors than traditional
dual-rail domino gates, they are in a small quantity (only 56,
used in the critical data path), which have small impact on
the transistor count.
The results also show that the transistor count of LP2/2-SR
is larger than that of synchronous pipeline, which indicatesthat conventional latchless pipelines are difficult to realize thepotential advantage of small silicon area. The main reason isthe dual-rail encoding overhead in domino data path. Becauseof the latchless feature, a lot of implicit storage elements (dualrail domino buffers) have to be added at each pipeline stage
to store data. These added dual-rail domino buffers cause alarge overhead. Although LP2/2-SR is significantly more area
efficient than LP2/2, it still consumes more transistors than
Sync and Sync-CG.
In addition to the transistor count, total FET width is a better
metric to figure the relative difference of capacitance between
designs. Table IV shows that APCDP, respectively, reduces
the total FET width by 34.8% and 39.3% compared with
LP2/2-SR and Sync. An interesting result is that LP2/2-SR
has a smaller total FET width even it has a larger transistor
count compared with Sync. This is because domino gates use
keepers to protect charge leakage problem [20]. These keepers
have a very small transistor size.

2) Latency: APCDP and LP22-SR have about one-third
lower forward latency than Sync and Sync-CG. This is because
latchless design has no sequential overhead (no registers
or latches) on its forward path. Compared with LP22-SR,
APCDP has a little larger latency. The latency is sacrificed
for constructing the stable critical data path. Fortunately, thisdegradation is not serious.
3) Throughput: The performances of throughput are evaluated without considering design margins, which are all ideal
results from the schematic simulations.
The results show that LP2/2-SR has the best throughput performance. This benefits from the bundled-data asynchronous
design of LP2/2-SR. Traditional dual-rail domino data paths in
LP2/2-SR actually have better signal transition speed than thedata paths composed of SLGs/SLGLs. Bundled-data design
can exploit this benefit to increase the pipeline throughput. However, delay margins need to be added in practicalbundled-data design, which would decrease the performanceof throughput.
Because of the dual-rail critical data path, APCDP
does not have to add design margins in practical design.
In Section III-D1, it shows that the pipeline structure of
APCDP originally supplies some time margins. Although
APCDP has a slower pipeline speed and a higher forward
latency than LP2/2-SR in the ideal evaluation, it is possiblethat APCDP may have a faster pipeline speed and a lower
latency than LP2/2-SR in practical design if the timing margins required in LP2/2-SR exceed the detection overhead in
APCDP. Especially, the delay of function blocks is not known
until the circuit layout has been generated. This can make theestimation of matching delay in LP2/2-SR overly conservativewith a negative impact on performance.
The throughputs of Sync and Sync-CG relate to the pipeline
granularity. Although the throughput performance can be
improved using fine-grain design, the power consumption
increases simultaneously. Therefore, Sync and Sync-CG are
carefully designed considering the tradeoff between throughput and power. Although Sync and Sync-CG have the same
throughput performance with APCDP, they hardly can win
APCDP in practical design because synchronous design has
to add design margins.
4) Power: The energy consumption of VLSI circuits relates
to the toggling rate in data paths. In APCDP, the adoption of
single-rail domino gates in the noncritical data paths saves not
only silicon area by reducing transistor count but also energy
consumption by reducing the toggling rate.
Fig. 13 shows the energy consumption per cycle forprocessing different data patterns. Each energy consumption is an average value calculated from 100 cycles. The
results show that APCDP consumes much less energy thanLP2/2-SR. The adoption of single-rail domino gates in APCDP
reduces the toggle rate in data paths since single-rail domino
logic does not toggle when transferring low-voltage signal.
Besides, the toggling rate relates to the injected data patterns.
Therefore, the energy consumption of APCDP varies a lot
according to different data patterns. On the other hand, theenergy consumption of LP2/2-SR remains almost constant.
LP2/2-SR’s full dual-rail domino data paths have almost a

XIA et al.: ASYNCHRONOUS DOMINO LOGIC PIPELINE DESIGN

629

C. Further Discussion

Fig. 15.

Workload definition.

constant toggling rate regardless of the injected data patterns.
Compared with LP2/2-SR, APCDP saves up to 60.2% ofenergy in the best case when processing data pattern ff*00(hexadecimal digit) and 24.5% of energy in the worst casewhen processing data pattern ff*ff.
The energy consumption of Sync-CG is also evaluated.
However, Sync-CG is designed using static logic. Different
from domino logic, static logic does not have an initial state.
To provide a relative fair comparison, we set the initial stateof Sync-CG as low-voltage inputs. The injected data patterns
are a certain data pattern (e.g., ff*ff) following with an initialpattern ff*00. The energy consumption per cycle is calculated
from 100 cycles. The results show that Sync-CG has lower
energy consumption than LP22-SR in most cases. However,Sync-CG also consumes more energy than LP2/2-SR when
the toggling rate is high (processing ff*ff). Since the toggling
rate in Sync-CG relates to the initial state, the practical energy
consumption might be better or even worse than the evaluatedresults. In our evaluated cases, APCDP shows better energy
consumption than Sync-CG.
Furthermore, the power performance with different workloads is evaluated. Fig. 14 shows the performance of power
consumption when all designs operate at 3.6G dataset/s. The
solid lines show the power consumption when the injected
data patterns are recurring between ff*ff ! ff*00. The dottedlines shows the power consumption when the injected data
patterns are recurring between ff*0f ! ff*00. The workloadrefers to the rate of the number of active-state cycles to thetotal number of cycles. In our case, the workload is calculated
based on a period of consecutive data injection cycles (activestate cycles) following consecutive empty cycles. Fig. 15
shows the workload definition. The workload is calculated
as N/(N + M), where N is the number of consecutive data
injection cycles and M is the number of consecutive empty
cycles.
The solid and dotted lines, respectively, show that APCDP
reduces the power by 41.6% and 52.9% compared with
LP2/2-SR. This evaluation also verifies that Sync and SyncCG have a better performance of power than LP2/2-SR in mostsituations, except for processing data pattern ff*ff. However,Sync and Sync-CG can hardly win APCDP. APCDP saves up
to 43.9% and 38.6% of power compared with Sync-CG when,respectively, processing ff*ff and ff*0f. In addition, the results
also show that Sync-CG saves a lot of clock power comparedwith Sync. However, because of the clock-gating design,
Sync-CG consumes a little more power than Sync when thecircuits work at peak speed.

The above evaluation is based on schematic simulation.
To apply APCDP to large function modules, design automation
is an important issue that has to be solved. Design automation
for asynchronous circuits is a very large research domain.
It is difficult to fully cover this topic. The interested reader isreferred to [21]. Here, we just simply address several specificdesign automation issues in APCDP.
One issue is the design automation for constructing astable critical data path. Based on the proposed construction
method, design automation flow can be easily developed. First,
the gate with the largest number of inputs in each stage andconnection of gates between stages is identified. Then, theproper gates using SLGs or SLGLs are replaced according to
the gate connection information and optimization methods.
Another issue is the design automation for layout. Standard
placement and routing (P&R) tools tend to reduce the worst
case delay in function blocks by optimizing circuit layout.
Such optimization is not suitable for APCDP since it would
degrade the robustness of the constructed critical data path. To
avoid this problem, a specific P&R method has to be developed
to increase the delay on the constructed path.
The last issue is timing verification. There are almost no
EDA support for verifying domino circuits because charge
sharing and uncertainty about worst case delay makes static
timing analysis (STA) very complex [21]. In APCDP, theknown critical data path and the dual-rail handshake control
logic help in easing the timing analysis problem. After creatinga high-quality domino gate library, it is possible to apply STA
for verifying the timing constraints in APCDP.
V. C ONCLUSION
This paper introduced a novel design method of asynchronous domino logic pipeline. The pipeline is realized based ona constructed critical data path. The design method greatly
reduces the overhead of handshake control logic as well asfunction block logic, which not only increases the pipeline
throughput but also decreases the power consumption. The
evaluation results show that the proposed design has better
performance than a bundled-data asynchronous domino logic
pipeline (LP2/2-SR). It is even comparable with a synchronous
pipeline with sequential clock gating.
R EFERENCES[1] B. H. Calhoun, Y. Cao, X. Li, K. Mai, L. T. Pileggi, and
R. A. Rutenbar, “Digital circuit design challenges and opportunities inthe era of nanoscale CMOS,” Proc. IEEE, vol. 96, no. 2, pp. 343–365,
Feb. 2008.
[2] J. Sparsø and S. Furber, Principles of Asynchronous Circuit Design:
A Systems Perspective. Boston, MA, USA: Kluwer, 2001.
[3] M. Krstic, E. Grass, F. K. Gurkaynak, and P. Vivet, “Globally asynchronous, locally synchronous circuits: Overview and outlook,” IEEE Des.
Test Comput., vol. 24, no. 5, pp. 430–441, Sep./Oct. 2007.
[4] A. J. Martin and M. Nystrom, “Asynchronous techniques for systemon-chip design,” Proc. IEEE, vol. 94, no. 6, pp. 1089–1120, Jun. 2006.
[5] J. Teifel and R. Manohar, “An asynchronous dataflow FPGA architecture,” IEEE Trans. Comput., vol. 53, no. 11, pp. 1376–1392, Nov. 2004.
[6] H. S. Low, D. Shang, F. Xia, and A. Yakovlev, “Variation tolerant
AFPGA architecture,” in Proc. ASYNC, 2011, pp. 77–86.

630

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, VOL. 23, NO. 4, APRIL 2015[7] M. Hariyama, S. Ishihara, and M. Kameyama, “Evaluation of a fieldprogrammable VLSI based on an asynchronous bit-serial architecture,” IEICE Trans. Electron., vol. E91-C, no. 9, pp. 1419–1426,
Sep. 2008.
[8] T. E. Williams, “Self-timed rings and their application to division,”
Ph.D. dissertation, Dept. Comput. Sci., Stanford Univ., Stanford, CA,
USA, Jun. 1991.
[9] A. M. Lines, “Pipelined asynchronous circuits,” Dept. Comput. Sci.,
California Inst. Technol., Pasadena, CA, USA, Tech. Rep., 1998.
[10] S. M. Nowick and M. Singh, “High-performance asynchronous pipelines
an overview,” IEEE Des. Test Comput., vol. 28, no. 5, pp. 8–22,
Sep./Oct. 2011.
[11] M. Singh and S. M. Nowick, “The design of high-performance dynamic
asynchronous pipelines: Lookahead style,” IEEE Trans. Very Large Scale
Integr. (VLSI) Syst., vol. 15, no. 11, pp. 1256–1269, Nov. 2007.
[12] M. Singh, J. A. Tierno, A. Rylyakov, S. Rylov, and S. M. Nowick, “Anadaptively pipelined mixed synchronous-asynchronous digital FIR filter
chip operating at 1.3 gigahertz,” IEEE Trans. Very Large Scale Integr.
(VLSI) Syst., vol. 18, no. 7, pp. 1043–1056, Jul. 2010.
[13] D. Harris, Introduction to CMOS VLSI Design—Lecture 9: Circuit
Families (Lecture Notes on the Subject). Claremont, CA, USA: Harvey
Mudd College, 2004.
[14] Z. Xia, S. Ishihara, M. Hariyama, and M. Kameyama, “Synchronising
logic gates for wave-pipelining design,” IEE Electron. Lett., vol. 46,
no. 16, pp. 1116–1117, Aug. 2010.
[15] S. Ahuja and S. Shukla, “MCBCG: Model checking based sequential
clock-gating,” in Proc. High Level Des. Validation Test Workshop, 2009,
pp. 20–25.
[16] L. Li, W. Wang, K. Choi, S. Park, and M.-K. Chung, “SeSCG:
Selective sequential clock gating for ultra-low-power multimedia mobile
processor,” in Proc. IEEE Int. Conf. EIT, May 2010, pp. 1–6.
[17] Z. Xia, S. Ishihara, M. Hariyama, and M. Kameyama, “Dual-rail/singlerail hybrid logic design for high-performance asynchronous circuit,” inProc. IEEE ISCAS, May 2012, pp. 3017–3020.
[18] Z. Xia, S. Ishihara, M. Hariyama, and M. Kameyama, “Design ofhigh-performance asynchronous pipeline using synchronizing logic
gates,” IEICE Trans. Electron., vol. E95-C, no. 8, pp. 1434–1443,
Aug. 2012.
[19] I. Sutherland, B. Sproull, and D. Harris, Logical Effort: Designing Fast
CMOS Circuits. San Mateo, CA, USA: Morgan Kaufmann, 1999.
[20] P. Srivastava, A. Pua, and L. Welch, “Issues in the design of domino
logic circuits,” in Proc. 8th Great Lakes Symp. VLSI, Feb. 1998,
pp. 108–112.
[21] A. Taubin, J. Cortadella, L. Lavagno, A. Kondratyev, and A. Peeters,“Design automation of real-life asynchronous devices and systems,”
Found. Trends Electron. Des. Autom., vol. 2, no. 1, pp. 1–133,
2007.

Zhengfan Xia received the B.E. degree in electronic and information engineering from the China
University of Geosciences, Beijing, China, and the
M.S. and Ph.D. degrees in information science fromTohoku University, Sendai, Japan, in 2008, 2011,
and 2014, respectively.
He is currently with the Toshiba Research andDevelopment Center, Japan. His current researchinterests include asynchronous circuits, computerarchitecture, and security.

Masanori Hariyama received the B.E. degree inelectronic engineering and the M.S. and Ph.D.
degrees in information science from Tohoku University, Sendai, Japan, in 1992, 1994, and 1997,
respectively.
He is currently an Associate Professor with the
Graduate School of Information Sciences, Tohoku
University. His current research interests include
VLSI computing for real-world application, such as
robots, high-level design methodology for VLSIs,
and reconfigurable computing.

Michitaka Kameyama received the B.E., M.E., andD.E. degrees in electronic engineering from Tohoku
University, Sendai, Japan, in 1973, 1975, and 1978,
respectively.
He has been a Professor with Tohoku University
since 1991, where he was the Dean of the Graduate
School of Information Sciences from 2010 to 2014.
His current research interests include intelligent integrated systems for real-world applications, advanced
VLSI architecture, and new-concept VLSI, including
multiple-valued VLSI computing.
Prof. Kameyama was a recipient of the Outstanding Paper Awards at
the IEEE International Symposiums on Multiple-Valued Logic in 1984,
1985, 1987, and 1989, the Technically Excellent Award from the Societyof Instrument and Control Engineers of Japan in 1986, the Outstanding
Transactions Paper Award from the Institute of Electronics, Information andCommunication Engineers in 1989, the Technically Excellent Award from the
Robotics Society of Japan in 1990, the Special Award at the 9th LSI Design of
the Year in 2002, and the Outstanding Paper Award at the IADIS International
Conference in 2013.