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K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.038-041
38 | P a g e
Efficient Clocking System Using Sequential Elements With Low
Power Consumption
K.Umadevi P.Vishnu B.Kailasam
M.TECH (ES) Assistant Professor ,SCET Assistant Professor
,VITS(N6)
ABSTRACT
Low power flip-flops which plays a vital
role for the design of low-power digital systems.
Flip flops and latches consume a large amount of
power due to redundant transitions and clocking
system. In addition, the energy consumed by low
skew clock distribution network is steadily
increasing and becoming a larger fraction of the
chip power. Almost, 30% - 60% of total power
dissipation in a system is due to flip flops and
clock distribution network. In order to achieve a
design that is both high performances while also
being power efficient, careful attention must be
paid to the design of flip flops and latches. We
survey a set of flip flops designed for low power
and High performance.
Keywords: Flip-flop, Low Power, Clocking system.
I. INTRODUCTION
In the past, the major concerns of the VLSI
designer were area, performance, cost and
reliability. Power consideration was mostly of only
secondary importance. In recent years, however, this
has begun to change and, increasingly, power is
being given comparable weight to area and speed
considerations. One of the important factors is that
excessive power consumption is becoming the
limiting factor in integrating more transistors on a
single chip or on a multiple-chip module. Unless
power consumption is dramatically reduced, the
resulting heat will limit the feasible packing and
performance of VLSI circuits [1], [2] and systems.
Most of the current designs are synchronous which
implies that flip-flops and latches are involved in
one way or another in the data and control paths.
One of the challenges of low power methodologies
for synchronous systems is the power consumption
of the flip-flops and latches. It is important to save
power in these flip-flops and latches without
compromising state integrity or performance.
Power Consumption is determined by several
factors including frequency f, supply voltage, data
activity, capacitance, leakage and short circuit
current.
P= Pdynamic + Pshort circuit + Pleakage
In the above equation, Pdynamic is called the
switching power p= αCv2f. Pshortcircuit is the short
circuit power which is caused by the finite rise and
fall time of input signals, resulting in both the pull
up network and pull down network to be ON for a
short period Pshort circuit = Ishort circuit * Vdd. Pleakage is
the leakage power. With supply voltage scaling
down, the threshold voltage also decreases to
maintain performance. However, this leads to the
exponential growth of the subthreshold leakage
current.
Pleakage current = Ileakage current * Vdd.
Based on the above factors, there are
various techniques for lowering the power
consumption shown as follows: In Double Edge
Triggering, Using half frequency on the clock
distribution network will save approximately half of
the power consumption on the clock distribution
network. However the flip-flop must be able to be
double clock edge triggered. Double clock edge
triggering method reduces the power by decreasing
frequency. Using a low swing voltage on the clock
distribution network can reduce the clocking power
consumption since power is a quadratic function of
voltage. To use low swing clock
Distribution, the flip-flop should be a low swing
flip- flop. The low swing method reduces the power
consumption by decreasing voltage.
There are two ways to reduce the switching
activity: conditional operation (eliminate redundant
data switching: conditional capture flip-flop
(CCFF)) or clock gating, conditional discharge flip-
flop (CDFF). In Conditional Operation, there are
redundant switching activities in the internal node.
When input stays at logic one, the internal node is
kept charging and discharging without performing
any useful computation. The conditional operation
technique is needed to avoid the redundant
switching. In Clock Gating, when a certain block is
idle, we can disable the clock signal to that block to
save power. Both conditional operation and clock
gating methods reduce power by decreasing
switching activity.
In Reducing Short Current Power, split
path can reduce the short current power, since p-
MOS and n-MOS are driven by separate signals. In
Reducing Capacity of Clock Load, 80% of non
clocked nodes have switching activity less than 0.1.
K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.038-041
39 | P a g e
This means reducing power of clocked nodes is
important since clocked node has 100% activity.
One effective way of low power design for clocking
system is to reduce clock capacity load by
minimizing number of clocked transistor. Any local
clock load reduction will also decrease the global
power consumption. This method reduces power by
decreasing clock capacity.
II. SURVEYED TECHNIQUE FOR
REDUCING CLOCK CAPACITY
Most of the flip-flops presented here are
dynamic in nature, and some internal nodes are
precharged and evaluated in each cycle without
producing any useful activity at the output when the
input is stable. Reducing this redundant switching
activity has a profound effect in reducing the power
dissipation, and in the literature many techniques
were presented for this purpose . A brief survey of
such techniques is conducted in this work, and the
main techniques were classified as follows:
2.1 Conditional Capture Flip Flop
Conditional Capture technique is proposed
for disabling redundant internal transitions. This
technique achieves significant power reduction at
little or no delay penalties. Motivation behind
Conditional Capture technique[3] is the observation
that considerable portion of power is consumed for
driving internal nodes even when the value of the
output is not changed (corresponding to low input
activities). It is possible to disable internal
transitions when it is detected that they will have no
effect on output. But the drawback is increased set-
up time for sampling zero (low level) and also
heavier load is presented to the Q output of the flip
flop.
2.2 Conditional Precharge Flip Flop
For overcoming the disadvantage in
Conditional Capture Flip Flop[3], Conditional pre-
charge flip flop is proposed One of the most
important contributions of this work is related to
preventing unconditional pre-charge operation of the
internal node, tightly connected to excessive power
dissipation of the circuit. This is accomplished by
controlling the return of internal node to inactive
(high) state, allowing the internal node to stay at low
level until input condition is changed. This approach
efficiently eliminates the unnecessary transitions of
the internal node as well as race condition at the
output. There are two main disadvantages: One is
introducing another critical path for low input level
capture. Another drawback is increasing the output
load due to the feedback, which although minimal
size transistor can be used, being out of the critical
path, can affect total propagation delay.
2.3 Conditional Discharge Flip Flop
Conditional Discharge Flip-flop (CDFF)[4]
not only reduces the internal switching activities,
but also generates less glitches at the output, while
maintaining the negative setup time and small Q-to-
output delay characteristics. With a data-switching
activity of 37.5%, this flip-flop can save up to 39%
of the energy with the same speed. In this Flip-flop,
the extra switching activity is eliminated by
controlling the discharge path when the input is
stable HIGH. In this scheme, an n-MOS Transistor
is inserted in the discharge path with the high-
switching activity. When the input undergoes a
LOW-to-HIGH transition, the output changes from
HIGH to LOW. This transition at the output
switches off the discharge path of the first stage to
prevent it from discharging or doing evaluation in
succeeding cycles as long as the input is stable. But
the disadvantage is it used 15 clocked transistors.
2.4 Conditional Data Mapping Flip Flop
Conditional Data Mapping Flip flop used
only seven clocked transistors, resulting in about
50% reduction in the number of clocked
transistors,hence CDMFF[5] used less power than
CCFF and CDFF as shown in fig 2.1.Note that
CDFF used double edge clocking. For simplicity
purposes, we did not include the power savings by
double edge triggering on the clock distribution
network. This shows the effectiveness of reducing
clocked transistor numbers to achieve low power,
Since CDMFF outperforms CCFF and CDFF. But it
makes very difficult to apply the Double edge
triggering and also it cannot be used in a low swing
environment. Moreover it reduces the number of
clocked transistors but it has redundant clocking as
well as floating node. So we can move into the
clocked pair shared flip-flop.
FIGURE 2.1:CDMFF.
K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.038-041
40 | P a g e
2.5 CLOCKED PAIR SHARED FLIP FLOP
(CPSFF)
Clocked Pair Shared flip-flop (CPSFF)[6]
to use less clocked transistor than CDMFF and to
overcome the floating problem in CDMFF as shown
in fig 2.2. In the clocked-pair-shared flip-flop,
clocked pair is shared by first and second stage. An
always on p-MOS, P1, is used to charge the internal
node rather than using the two clocked pre charging
transistors (P1,P2) in CDMFF. Comparing with
CDMFF, a total of three clocked transistors are
reduced, such that the clock load seen by the clock
driver is decreased, resulting in an efficient design.
CPSFF uses four clocked transistors rather than
seven clocked transistors in CDMFF, resulting in
approximately 40% reduction in number of clocked
transistors.
Figure 2.2: Clocked Pair Shared Flip Flop
III. Proposed Low Power Clocked Pass
Transistor Flip-Flop Design
By using the Pass Transistor Logic family
idea we are designing this circuit as well as by using
the pass transistor logic we are using only one
clocking transistor so it will be Consuming only less
power in the clock network of the Flip flop when
compared to all other circuits.
As well as we are having only 6 Transistors
excluding the not gates also. So we will be having
much reduced power and area when compared to the
other two designs. At the same time due to the
reduced no of transistor count we can reduce the
delay oriented things also. Thus we are reducing the
overall switching delay and power, area
consumption. So this circuit will be acting as good
sequential elements when compared to other flip-
flop design.
The graph represents the input & output
characteristics of our proposed system from that we
can clearly understand how it works as negative
edge triggered flip-flop. There is some nano seconds
delay is there even though it’s a negligible amount
only. Those delays can be further reduced by
reducing the sizes of the transistor we are using in
this circuit. Or by reducing the nano meter
technology also we can reduce the constraints. The
Layout design of the proposed new flip-flop is
shown in the figure 3.2 the area of that is mentioned
at the downside of the layout.
Figure 3.1: Proposed Low Power Clocked Pass
Transistor flip-floP
Figure 3.2: Layout of theLCPTFF Proposed Design
Thus the Our Proposed Low Power
Clocked Pass Transistor flip-flop (LCPTFF Fig.3.1)
design shows much less power & Area constraints
than the Existing two Flip-Flop designs. As well as
the Proposed design will be having very less clock
delay when compared to all other circuits. So it can
be used in all the future sequential elements for high
speed low SOC’c manufacturing.
K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.038-041
41 | P a g e
III. Tabulation
Power & Area Comparison Table using
CMOS012 um
FLIP
FLOP
No. of
Transist
or
Power
Consumpt
ion
Area
Consumpti
on
Width
CDMF
F
7 11.380µW 278.1µm2 31.3µ
m
CPSFF 4 6.184µW 207.8µm2 22.2µ
m
LCPT
FF
4 4.663 µW 138.1µm2 16.4µ
m
Thus the Our Proposed Low Power
Clocked Pass Transistor flip-flopdesign shows much
less power & Area constraints than the Existing two
Flip-Flop designs. As well as the Proposed design
will be having very less clock delay when compared
to all other circuits. So it can be used in all the
future sequential elements for high speed low
SOC’c manufacturing.
IV. CONCLUSION
In this paper, a variety of design techniques
for low power clocking system are reviewed. One
effective method, reducing capacity of the clock
load by minimizing number of clocked transistor, is
elaborated. Following the approach, one novel
CPSFF is proposed, which reduces local clock
transistor number by about 40%. In view of power
consumption of clock driver, the new CPSFF
outperforms prior arts in flip-flop design by about
24%. Furthermore, several low power techniques,
including low swing and double edge clocking, can
be explored to incorporate into the new flip-flop to
build clocking systems.
REFERENCES
[1] C. L. Kim and S. Kang, “A low-swing
clock double edge-triggered flip-flop,”
IEEE J. Solid-State Circuits, vol. 37, no. 5,
pp. 648–652, May 2002.
[2] J. Rabaey, A. Chandrakasan, and B.
Nikolic, Digital Integrated Circuits.
Englewood Cliffs, NJ: Prentice-Hall, 2003.
[3] B. Kong, S. Kim, and Y. Jun, “Conditional
capture flip-flop for statistical power
reduction,” IEEE J. Solid-State Circuits,
vol. 36, no. 8, pp.1263–1271, Aug. 2001.
[4] P. Zhao, T. Darwish, and M. Bayoumi,
“High-performance and lowpower
conditional discharge flip-flop,” IEEE
Trans. Very Large Scale Integr. (VLSI)
Syst., vol. 12, no. 5, pp. 477–484, May
2004.
[5] C. K. Teh, M. Hamada, T. Fujita, H. Hara,
N. Ikumi, and Y. Oowaki, “Conditional
data mapping flip-flops for low-power and
high-performance systems,” IEEE Trans.
Very Large Scale Integr. (VLSI) Syst.,vol.
14, no. 12, pp. 1379–1383, Dec. 2006.
[6] Peiyi Zhao, Jason McNeely,
WeidongKuang, Nan Wang, and“Design of
Sequential Elements for Low
PowerClocking System” IEEE Transaction
May 2011

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Efficient Low Power Clocking System Using Sequential Elements

  • 1. K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.038-041 38 | P a g e Efficient Clocking System Using Sequential Elements With Low Power Consumption K.Umadevi P.Vishnu B.Kailasam M.TECH (ES) Assistant Professor ,SCET Assistant Professor ,VITS(N6) ABSTRACT Low power flip-flops which plays a vital role for the design of low-power digital systems. Flip flops and latches consume a large amount of power due to redundant transitions and clocking system. In addition, the energy consumed by low skew clock distribution network is steadily increasing and becoming a larger fraction of the chip power. Almost, 30% - 60% of total power dissipation in a system is due to flip flops and clock distribution network. In order to achieve a design that is both high performances while also being power efficient, careful attention must be paid to the design of flip flops and latches. We survey a set of flip flops designed for low power and High performance. Keywords: Flip-flop, Low Power, Clocking system. I. INTRODUCTION In the past, the major concerns of the VLSI designer were area, performance, cost and reliability. Power consideration was mostly of only secondary importance. In recent years, however, this has begun to change and, increasingly, power is being given comparable weight to area and speed considerations. One of the important factors is that excessive power consumption is becoming the limiting factor in integrating more transistors on a single chip or on a multiple-chip module. Unless power consumption is dramatically reduced, the resulting heat will limit the feasible packing and performance of VLSI circuits [1], [2] and systems. Most of the current designs are synchronous which implies that flip-flops and latches are involved in one way or another in the data and control paths. One of the challenges of low power methodologies for synchronous systems is the power consumption of the flip-flops and latches. It is important to save power in these flip-flops and latches without compromising state integrity or performance. Power Consumption is determined by several factors including frequency f, supply voltage, data activity, capacitance, leakage and short circuit current. P= Pdynamic + Pshort circuit + Pleakage In the above equation, Pdynamic is called the switching power p= αCv2f. Pshortcircuit is the short circuit power which is caused by the finite rise and fall time of input signals, resulting in both the pull up network and pull down network to be ON for a short period Pshort circuit = Ishort circuit * Vdd. Pleakage is the leakage power. With supply voltage scaling down, the threshold voltage also decreases to maintain performance. However, this leads to the exponential growth of the subthreshold leakage current. Pleakage current = Ileakage current * Vdd. Based on the above factors, there are various techniques for lowering the power consumption shown as follows: In Double Edge Triggering, Using half frequency on the clock distribution network will save approximately half of the power consumption on the clock distribution network. However the flip-flop must be able to be double clock edge triggered. Double clock edge triggering method reduces the power by decreasing frequency. Using a low swing voltage on the clock distribution network can reduce the clocking power consumption since power is a quadratic function of voltage. To use low swing clock Distribution, the flip-flop should be a low swing flip- flop. The low swing method reduces the power consumption by decreasing voltage. There are two ways to reduce the switching activity: conditional operation (eliminate redundant data switching: conditional capture flip-flop (CCFF)) or clock gating, conditional discharge flip- flop (CDFF). In Conditional Operation, there are redundant switching activities in the internal node. When input stays at logic one, the internal node is kept charging and discharging without performing any useful computation. The conditional operation technique is needed to avoid the redundant switching. In Clock Gating, when a certain block is idle, we can disable the clock signal to that block to save power. Both conditional operation and clock gating methods reduce power by decreasing switching activity. In Reducing Short Current Power, split path can reduce the short current power, since p- MOS and n-MOS are driven by separate signals. In Reducing Capacity of Clock Load, 80% of non clocked nodes have switching activity less than 0.1.
  • 2. K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.038-041 39 | P a g e This means reducing power of clocked nodes is important since clocked node has 100% activity. One effective way of low power design for clocking system is to reduce clock capacity load by minimizing number of clocked transistor. Any local clock load reduction will also decrease the global power consumption. This method reduces power by decreasing clock capacity. II. SURVEYED TECHNIQUE FOR REDUCING CLOCK CAPACITY Most of the flip-flops presented here are dynamic in nature, and some internal nodes are precharged and evaluated in each cycle without producing any useful activity at the output when the input is stable. Reducing this redundant switching activity has a profound effect in reducing the power dissipation, and in the literature many techniques were presented for this purpose . A brief survey of such techniques is conducted in this work, and the main techniques were classified as follows: 2.1 Conditional Capture Flip Flop Conditional Capture technique is proposed for disabling redundant internal transitions. This technique achieves significant power reduction at little or no delay penalties. Motivation behind Conditional Capture technique[3] is the observation that considerable portion of power is consumed for driving internal nodes even when the value of the output is not changed (corresponding to low input activities). It is possible to disable internal transitions when it is detected that they will have no effect on output. But the drawback is increased set- up time for sampling zero (low level) and also heavier load is presented to the Q output of the flip flop. 2.2 Conditional Precharge Flip Flop For overcoming the disadvantage in Conditional Capture Flip Flop[3], Conditional pre- charge flip flop is proposed One of the most important contributions of this work is related to preventing unconditional pre-charge operation of the internal node, tightly connected to excessive power dissipation of the circuit. This is accomplished by controlling the return of internal node to inactive (high) state, allowing the internal node to stay at low level until input condition is changed. This approach efficiently eliminates the unnecessary transitions of the internal node as well as race condition at the output. There are two main disadvantages: One is introducing another critical path for low input level capture. Another drawback is increasing the output load due to the feedback, which although minimal size transistor can be used, being out of the critical path, can affect total propagation delay. 2.3 Conditional Discharge Flip Flop Conditional Discharge Flip-flop (CDFF)[4] not only reduces the internal switching activities, but also generates less glitches at the output, while maintaining the negative setup time and small Q-to- output delay characteristics. With a data-switching activity of 37.5%, this flip-flop can save up to 39% of the energy with the same speed. In this Flip-flop, the extra switching activity is eliminated by controlling the discharge path when the input is stable HIGH. In this scheme, an n-MOS Transistor is inserted in the discharge path with the high- switching activity. When the input undergoes a LOW-to-HIGH transition, the output changes from HIGH to LOW. This transition at the output switches off the discharge path of the first stage to prevent it from discharging or doing evaluation in succeeding cycles as long as the input is stable. But the disadvantage is it used 15 clocked transistors. 2.4 Conditional Data Mapping Flip Flop Conditional Data Mapping Flip flop used only seven clocked transistors, resulting in about 50% reduction in the number of clocked transistors,hence CDMFF[5] used less power than CCFF and CDFF as shown in fig 2.1.Note that CDFF used double edge clocking. For simplicity purposes, we did not include the power savings by double edge triggering on the clock distribution network. This shows the effectiveness of reducing clocked transistor numbers to achieve low power, Since CDMFF outperforms CCFF and CDFF. But it makes very difficult to apply the Double edge triggering and also it cannot be used in a low swing environment. Moreover it reduces the number of clocked transistors but it has redundant clocking as well as floating node. So we can move into the clocked pair shared flip-flop. FIGURE 2.1:CDMFF.
  • 3. K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.038-041 40 | P a g e 2.5 CLOCKED PAIR SHARED FLIP FLOP (CPSFF) Clocked Pair Shared flip-flop (CPSFF)[6] to use less clocked transistor than CDMFF and to overcome the floating problem in CDMFF as shown in fig 2.2. In the clocked-pair-shared flip-flop, clocked pair is shared by first and second stage. An always on p-MOS, P1, is used to charge the internal node rather than using the two clocked pre charging transistors (P1,P2) in CDMFF. Comparing with CDMFF, a total of three clocked transistors are reduced, such that the clock load seen by the clock driver is decreased, resulting in an efficient design. CPSFF uses four clocked transistors rather than seven clocked transistors in CDMFF, resulting in approximately 40% reduction in number of clocked transistors. Figure 2.2: Clocked Pair Shared Flip Flop III. Proposed Low Power Clocked Pass Transistor Flip-Flop Design By using the Pass Transistor Logic family idea we are designing this circuit as well as by using the pass transistor logic we are using only one clocking transistor so it will be Consuming only less power in the clock network of the Flip flop when compared to all other circuits. As well as we are having only 6 Transistors excluding the not gates also. So we will be having much reduced power and area when compared to the other two designs. At the same time due to the reduced no of transistor count we can reduce the delay oriented things also. Thus we are reducing the overall switching delay and power, area consumption. So this circuit will be acting as good sequential elements when compared to other flip- flop design. The graph represents the input & output characteristics of our proposed system from that we can clearly understand how it works as negative edge triggered flip-flop. There is some nano seconds delay is there even though it’s a negligible amount only. Those delays can be further reduced by reducing the sizes of the transistor we are using in this circuit. Or by reducing the nano meter technology also we can reduce the constraints. The Layout design of the proposed new flip-flop is shown in the figure 3.2 the area of that is mentioned at the downside of the layout. Figure 3.1: Proposed Low Power Clocked Pass Transistor flip-floP Figure 3.2: Layout of theLCPTFF Proposed Design Thus the Our Proposed Low Power Clocked Pass Transistor flip-flop (LCPTFF Fig.3.1) design shows much less power & Area constraints than the Existing two Flip-Flop designs. As well as the Proposed design will be having very less clock delay when compared to all other circuits. So it can be used in all the future sequential elements for high speed low SOC’c manufacturing.
  • 4. K.Umadevi, P.Vishnu, B.Kailasam / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 3, May-Jun 2013, pp.038-041 41 | P a g e III. Tabulation Power & Area Comparison Table using CMOS012 um FLIP FLOP No. of Transist or Power Consumpt ion Area Consumpti on Width CDMF F 7 11.380µW 278.1µm2 31.3µ m CPSFF 4 6.184µW 207.8µm2 22.2µ m LCPT FF 4 4.663 µW 138.1µm2 16.4µ m Thus the Our Proposed Low Power Clocked Pass Transistor flip-flopdesign shows much less power & Area constraints than the Existing two Flip-Flop designs. As well as the Proposed design will be having very less clock delay when compared to all other circuits. So it can be used in all the future sequential elements for high speed low SOC’c manufacturing. IV. CONCLUSION In this paper, a variety of design techniques for low power clocking system are reviewed. One effective method, reducing capacity of the clock load by minimizing number of clocked transistor, is elaborated. Following the approach, one novel CPSFF is proposed, which reduces local clock transistor number by about 40%. In view of power consumption of clock driver, the new CPSFF outperforms prior arts in flip-flop design by about 24%. Furthermore, several low power techniques, including low swing and double edge clocking, can be explored to incorporate into the new flip-flop to build clocking systems. REFERENCES [1] C. L. Kim and S. Kang, “A low-swing clock double edge-triggered flip-flop,” IEEE J. Solid-State Circuits, vol. 37, no. 5, pp. 648–652, May 2002. [2] J. Rabaey, A. Chandrakasan, and B. Nikolic, Digital Integrated Circuits. Englewood Cliffs, NJ: Prentice-Hall, 2003. [3] B. Kong, S. Kim, and Y. Jun, “Conditional capture flip-flop for statistical power reduction,” IEEE J. Solid-State Circuits, vol. 36, no. 8, pp.1263–1271, Aug. 2001. [4] P. Zhao, T. Darwish, and M. Bayoumi, “High-performance and lowpower conditional discharge flip-flop,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 12, no. 5, pp. 477–484, May 2004. [5] C. K. Teh, M. Hamada, T. Fujita, H. Hara, N. Ikumi, and Y. Oowaki, “Conditional data mapping flip-flops for low-power and high-performance systems,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst.,vol. 14, no. 12, pp. 1379–1383, Dec. 2006. [6] Peiyi Zhao, Jason McNeely, WeidongKuang, Nan Wang, and“Design of Sequential Elements for Low PowerClocking System” IEEE Transaction May 2011