Design of Power Efficient 4x4 Multiplier Based On Various Power Optimizing Techniques

Asian Journal of Applied Science and Technology (AJAST)
Volume 1, Issue 2, Pages 115-119, March 2017
© 2017 AJAST All rights reserved. www.ajast.net
Page | 115
Design of Power Efficient 4x4 Multiplier Based On Various Power Optimizing
Techniques
A.Venkatesh1
, N.Rathan2
and R.Saranya3
1Assistant Professor, Department of Electronics and Communication Engineering, Hindusthan Institute of Technology, Coimbatore, India.
Article Received: 21 February 2017 Article Accepted: 11 March 2017 Article Published: 13 March 2017
1. INTRODUCTION
The purpose of low power electronics is to compress complex
electronic circuits in minimum area with reduction in power
dissipation and delay. The power requirements of these
devices have increased many folds with the increase in
complexity of ICs. The need of transistors in VLSI design is
duly elucidated by Moore’s Law [1]. Reducing the transistor
count and power of circuits have been focus of researchers for
so many years and is still continuing [2]. Now-a-days logic
circuits are designed using pass transistor logic techniques
[3]. Recently many techniques have been proposed with the
objective of improving speed and power Consumption. The
Double Pass-Transistor Logic, developed by Hitachi
demonstrated a 1.5ns, 32-bit ALU in 0.25μm CMOS
technology and 4.4ns, 54X54 bit multiplier. Similarly many
works have been done recently to design 4x4 bit multiplier.
The main objective of our work is to implement the low power
high speed multiplier based on Sleepy Stack & to make a
detailed comparative study with conventional CMOS
multiplier. Our multiplier uses less number of transistors in
comparison to the conventional multiplier; so that the
propagation delay time & power consumption gets reduced. It
also helps in reducing the layout area thereby decreasing the
entire size of a module where this multiplier sub module is
used. With the objective of further reducing the POWER a
novel design of a Sleepy Stack technique is proposed in the
current paper.
2. DESIGN OF 4x4 MULTIPLIER
A combinational multiplier is a superior model Show casing
how simple logic functions (gates, half adders and full adders)
can be combined to build a much more complex function.
Consider the following example (fig. 1) for binary
multiplication of two positive 4-bit integer values. Here, each
bit in the multiplier is multiplied with the multiplicand. Each
of the four products is aligned (shifted left) according to the
position of the bit in the multiplier that is being multiplied
with the multiplicand.
Here, each bit in the multiplier is multiplied with the
multiplicand. Each of the four products is aligned (shifted
left) according to the position of the bit in the multiplier that is
being multiplied with the multiplicand. The four resulting
products are added to form the final result. Therefore for an
NxN multiplier, the result is 2N bits wide. With binary
numbers, forming the products is much easy. If the multiplier
bit is a 1, then the corresponding product is simply an
appropriately shifted copy of the multiplicand. If the
multiplier bit is a zero, then the product is zero. 1-bit binary
multiplication is thus just an AND operation.
Fig.1. Binary multiplication example (4x4)
To build the NxN multiplier let us take an array of a building
block consisting of an AND gate and a full adder to get the
partial product. The building block is shown in fig. 2 and the
4x4 multiplier in fig. 3 correspondingly. The basic building
block consists of an AND gate for computing locally the
corresponding partial product (X.Y), an input passed into the
block from above (Sum In), and a carry (Cin) passed from a
block diagonally above. It generates a carry out bit (COUT)
and a new sum out bit (Sum Out). Fig. 3 illustrates the
interconnection of these building blocks to construct a 4x4
combinational multiplier. The Ai values are distributed along
block diagonals, and the Bi values are passed along the rows.
ABSTRACT
In this paper, we propose a new technique for implementing a low power high speed multiplier based on Sleepy Stack Technique and consisting of
minimum number of transistors. Multiplier circuits are used comprehensively in Application Specific Integrated Circuits (ASICs). An 4 bit x 4 bit
multiplier has also been implemented using the design of only using basic combinational circuits and its performance has been analyzed and
compared with similar multipliers designed with peer combinational design available in literature. The explored method of implementation achieves
a high speed low power design for the multiplier. Simulated results indicate the superior performance of the proposed technique over conventional
CMOS multiplier. Detailed comparison of simulated results for the conventional and present method of implementation is presented.
Index Terms: 8-T Full Adder, 4x4 Multiplier, 2-T MUX, Pass transistor logic, 3-T XOR and Sleepy Stack.

Page | 116
Fig.2. Building block of multiplier
Fig. 3. 4x4 multiplier using AND gate, Half adder and full
adder
To design a low power 4x4 multiplier the approach is to
design the circuits with minimum nos. of transistors. Here the
basic building blocks (half adder, full adder & AND gate) of
the 4x4 multiplier shown in fig. 3 are constructed with
minimum no of transistors which are discussed in section 3.
3. ARCHITECTURE OF 8-T FA, 2-T AND GATE 3-T
XOR GATE & 5-T HA
This work presents adder circuits using pass transistor logic
based MUX & XOR gate, which contains lesser no. of
transistors and achieving better performance. This full adder
using pass transistor logic has advantages over CMOS and is
characterized by excellent speed and low power. In
electronics, Pass-Transistor-Logic (PTL) describes several
logic families used in the design of integrated circuits. It
reduces the count of transistors used to make different logic
circuits, by eliminating redundant transistors. Transistors are
used as switches to pass logic levels between nodes of a
circuit, instead of as switches connected directly to supply
voltages. This reduces the number of active devices, but has
the disadvantage that output levels can be no higher than the
input level. Each transistor in series has a lower voltage at its
output than at its input. For proper operation, design rules
define the arrangement of circuits, so that sneak paths, charge
sharing, and slow switching can be avoided. Double Pass
transistor Logic (DPL) eliminates some of the inverter stages
required for Complementary-Pass-transistor- Logic (CPL) by
using both N and P channel transistors, with dual logic paths
for every function. While it has high speed due to low input
capacitance, it has only limited capacity to drive a load. Pass
transistor logic has become important for the design of
low-power high-performance digital circuits due to the
smaller node capacitances and reduced transistors count it
offers. However, the acceptance and application of this logic
depends on the availability of supporting automation tools,
e.g. timing simulators, which can accurately analyse the
performance of large circuits at a speed, significantly faster
than that of SPICE based tools.
3.1 8-T Full Adder (FA)
The proposed 2T XOR gate has been used to design a 6T full
adder. The two outputs SUM and CARRY (𝐶𝑜𝑢𝑡) can be
generated based on the Boolean equations of full adder as
follows:
𝑆𝑢𝑚 = 𝐴⨁𝐵⨁𝐶𝑖𝑛
𝐶𝑜𝑢𝑡 = 𝐵.𝐶𝑖𝑛 + 𝐶𝑖𝑛.𝐴 + 𝐴.𝐵 = 𝐶𝑖𝑛. (𝐴⨁𝐵) + 𝐴.𝐵
The logic circuit of typical full adder is given in Figure 4. The
exclusive O Ring realized using wired logic of 3T XOR gate
as depicted in equation give rise to sum output and the final
carry output is given by using M1 and M2 pass transistors
given by equation. The W/L ratio of M3 and M4 transistors
are W=300 nm, L=60 nm in 65-nm technology. The W and L
of transistors from M1 to M4 is same as defined for XOR
gates. The schematic of the proposed 8 transistor full adder is
shown in Figure 9. A reverse bias voltage of 320 mV is kept in
order to concisely represent the appropriate logic high and
logic low levels in the output of simulated circuit. Evidently,
for the three input combination there is two stages delay for
the sum and carry output and the delay for carry output is less
than then As two XOR gates are used with reverse bias, there
is decline in the logic level with the cascading of exclusive
OR gates mainly perturbed at A=1 and B=1. The approach of
using minimum width and length is for minimizing the power
consumption in the circuit.
Fig. 4. Logic circuit of full adder
The first component required to design a full adder with 8
transistors is XOR gate. Conventional XOR gate can be
fabricated using Transmission Gate (TG) logic which needs
more than 3 transistors. But here is the design of a XOR gate

Page | 117
with 3 transistors as shown in fig.5 below. The second
component required to design a full adder with 2 XOR gate to
implement the sum out & another two input MUX to
implement the carry out. The basic structure of the 2:1 MUX
using pass gate transistor logic and implement sleepy stack
technique is shown in fig. 8. In this configuration we have
connected PMOS and NMOS along with a SEL line, as in
MUX.
Fig. 5. Basic view of 3T XOR gate
Fig.6. Basic view of 2T MUX
Sleepy Stack Approach
The sleepy stack technique divides existing transistors into
two half size transistors like the stack approach. Then sleep
transistors are added in parallel to one of the divided
transistors.
Fig.7. Sleepy Stack Approach
Figure 7 shows its structure. During sleep mode, sleep
transistors are turned off and stacked transistors suppress
leakage current while saving state.
Each sleep transistor, placed in parallel to the one of the
stacked transistors, reduces resistance of the path, so delay is
decreased during active mode.
However, area penalty is a significant matter for this approach
since every transistor is replaced by three transistors and since
additional wires are added for S and S‟, which are sleep
signals.
It reduces noise and power so we implement the sleepy stack
technique in AND gate. For build a more efficient 4x4
multiplier. Basic view of sleepy stack technique using And
gate shown in figure.
Fig. 8. Basic view of 2T MUX with Sleepy Stack Approach
Using 2 input MUX & 2 input XOR gate we can design a 8-T
FA as shown in fig. 9 below,
Fig. 9. 8-T FA based on MUX & XOR gates
3.2 5-T Half Adder (HA)
As already we have designed 3-T XOR and 2-T AND gate,
now one half adder can be easily designed with five nos. of
transistors. Fig. 10 shows 5-T half adder block diagram.

Page | 118
Fig.10. 5-T HA based 3T XOR & 2T AND
There are three major sources of power dissipation in a digital
CMOS circuit: logic transition, short-circuit current and
leakage current. The short-circuit current is the direct current
passing through the supply and the ground, when both the
NMOS and the PMOS transistors are simultaneously active.
As the proposed 8-T FA and 5T HA do not direct connections
to or port (voltage connections to the back gate terminals are
not considered), the probability of a direct path formation
from positive voltage supply to the ground during switching
can be substantially reduced that is, and the power
consumption due to short circuit current is considered
negligibly small.
Furthermore, in the new adder circuits, all of its internal gate
nodes are directly excited by the fresh input signals (and),
leading to a much faster transition (low rise and fall times) in
its output signals. As a result, the power consumption of the
following buffer stage can benefit from faster/cleaner Sum
and Cout outputs.
4. SIMULATION RESULTS & ANALYSIS
For testing the proposed multiplier we provide the input
combinations as bit parameter of example shown in fig. 1. All
the combinations are introduced during the time period
between 10ns to 20ns.
Thus for the outputs we also concentrate over that particular
time period only. We run the simulation over both
conventional & proposed two different multipliers
architecture. The transient responses of all the circuits are
shown below in fig.11 & fig.12 respectively. After running
the simulation the power consumption and delay of the
circuits are tested and compared.
From the simulation it can be easily understood that the
proposed multipliers have the same functional response as
like the conventional multiplier. The power & timing
behaviour is tabulated in the table 1,
Regarding area consideration it can be easily understood that
with lesser no. of transistor count compared with conventional
circuit multiplier core will be much lower size compared to
10x16-T 4x4 multiplier and 34x16-T CMOS 4x4 multiplier.
Fig. 11 Transient response of 90-T conventional 4x4
Multiplier Ai: one multiplicand input (4 bits), Bi: one
multiplier input (4 bits), Pi: partial product
Fig. 12 Transient response of proposed 4x4 Multiplier Ai: one
multiplicand input (4 bits), Bi: one multiplier input (4 bits),
Pi: partial product.

Page | 119
Table 1. Comparison between Conventional & Proposed
Multiplier
Fig. 13. Power consumption of (a) conventional CMOS
multiplier; (b) Power consumption of conventional 90-T
multiplier and (c) proposed 4x4 multiplier.
5. CONCLUSION
From the above results it can be concluded that our proposed
multiplier has got better performance in terms of speed, power
and area consideration in comparison with the conventional
CMOS multiplier. It turns out that in contrast to older process
technologies, this approach is more suitable for industrial
usage in advanced process technologies.
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Design of Power Efficient 4x4 Multiplier Based On Various Power Optimizing Techniques

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Design of Power Efficient 4x4 Multiplier Based On Various Power Optimizing Techniques