Circuits and Systems, 2016, 7, 630-642
Published Online May 2016 in SciRes.
How to cite this paper: Saravanan, S., Vennila, I. and Mohanram, S. (2016) Design and Implementation of Efficient Reversi-
ble Arithmetic and Logic Unit. Circuits and Systems, 7, 630-642.
Design and Implementation of Efficient
Reversible Arithmetic and Logic Unit
Subramanian Saravanan1*, Ila Venni la1, Sudha Mohanram2
1Department of EEE, P. S. G. College of Technology, Coimbatore, India
2Sri Eshwar College of Engineering, Kondampatty, Coimbatore, India
Received 11 March 2016; accepted 6 May 2016; published 11 May 2016
Copyright © 2016 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativ ecommon icenses/by /4.0/
In computing architecture, ALU plays a major role. Many promising applications are possible with
ATMEGA microcontroller. ALU is a part of these microcontrollers. The performance of these mi-
crocontrollers can be improved by applying Reversible Logic and Vedic Mathematics. In this paper,
an efficient reversible Arithmetic and Logic Unit with reversible Vedic Multiplier is proposed and
the simulation results show its effectiveness in reducing quantum cost, number of gates, and the
total number of logical calculations.
Reversible Logic Gates, Reversible Logic Circuits, Reversible Multiplier Circuits, Vedic Multiplier,
1. Introduction
Moore’s law states that number of transistors in a chip doubles every two years but chip size decreases. This
cannot be reduced greatly which will lead to more power consumption. This paves the path to ne w technologies
“Reversible Logic and Quantum Dot Cell ular Automata(QCA). As stated b y Launder irreversible logic (un-
equal number of inputs and outputs) consumes more power [1]. To overcome this problem Bennett sets equal
number of inputs and outputs, which will dissipate less po wer as input bits are preserved at the output [2]. T his
is called Reversible Logi c. I n this p ap er , Reversible Lo gic is chosen for its low power and Vedic concept is used
for its faster arithmetic calculations. A quantum computer uses principle of superposition and entangleme nt for
qubit (quantum bit-basic unit of information in quantu m computers) computation. Quantum computers are faster
than classical computer and will find its application in air craft tester, driverless cars and develop more effective
Corresponding author.
S. Saravanan et al.
drugs, etc. Reversible Logic plays an important role in converting classical computation to quantum computa-
tion. The b a sic properties of Re ver sib le Logic are discussed in [3].
Reversible gates are classified as 2 × 2 gates, 3 × 3 gates and 4 × 4 gates. The classification of Reversible
Logic gates is given in Figure 1.
The basic reversible gates are Feynman gate, Taffoli gate and Peres gate. The basic reversible gates are shown
in Figure 2 [4].
The 4 × 4 reversible gates such as TSG gate and HNG gate are discussed in [3] given below.
TSG Gate
Thapliyal proposed a 4 × 4 reversible gate called TSG gate [5]. The TSG gate is shown in Figure 3 and
quantum circuit diagram for TSG gate is given in Figure 4. The input and output functions are given i n Equa-
tions (1) and (2) respectively.
( )
Iv A,B,C,D=
() ()
( )
′′ ′′′ ′′′ ′
= ==⊕=⊕⊕=⊕⋅⊕⊕
Full adder, Wallace tree multiplier 4:2 compressor are constructed using TSG gate.
Figure 1 . Classification of reversible logic gates.
Figure 2 . Bas ic reversible gat es .
Figure 3 . T SG gate.
S. Saravanan et al.
Figure 4 . Quantum circuit diagram for TSG gate.
Single TSG gate will act as full adder. Parallel adder or ripple carry adder is implemented using the same.
Ripple carry adder is needed in multiplier. When C input is 0, D input is given with carry input, and then TSG
gate functions as full adder. The TSG gate as full adder is shown in Figure 5.
HNG Gate
It is a 4 × 4 reversible gate [6]. The HNG gate is shown in Figure 6 and quantum circuit diagram for HNG
gate is given in Figure 7. The input and outp ut func tions are given in Equa tions (3) and (4) respectively.
( )
Iv A,B,C,D=
HNG ga te is use d to c onstruc t full adder and multiplier. When D input is 0, A, B and C in puts ar e give n, and
then HNG gate functions as full adder. The HNG gate as full adder is shown in Figure 8.
The basic benchmark parameters of the reversible logic circuits are quantum cost, garbage output, and total
number of logical calculations .
The nu mber o f reversible logic gates either 1 × 1, 2 × 2, 3 × 3 or 4 × 4 needed to design a reversible system is
called number of gates. Quantum cost (QC) refers to the number of elementary gates 1 × 1 or 2 × 2 reversible
logic gates needed to design the reversible logic circuit.
The unused output in a reversible circuit is called garbage output.
Tota l logic calculation is the n umber o f XO R, AND, and N OT logic functio ns used i n the re versible cir c uit. α
indicates number of XOR logic in the circuit, β indicates number of AND logic in the circuit and d indicates
number of NOT logic in the circui t
Research in reversible logic is getting important today. Thapliyal and Srinivasan proposed a new reversible
TSG gate [5] and d is cussed about reversible carry look-ahead adder and other adder architecture which formed a
part of ALU. The quantum cost of TSG gate is quiet high when compared to HNG gate. Haghparast proposes
two new 4 × 4 bit reversible multiplier designs with less hardware complexity, less garbage bits, less quantum
cost, and le ss co nsta nt inp uts [6] and the architecture uses Peres gate for partial product generation. But the total
logical calculation is more due to extra logics in Peres gate. Research is going on in deriving more applications
out of it. Research is moving towards deriving a new application from reversible gates. Ancient Indians fol-
lowed some sutras or formulae for mathematical computation. These basic mathematical calculations form the
base for modern VLSI architecture. Thapliyal discussed about performance of Vedic Multipliers on FPGA [7]
and discussed the irreversible architecture based on delay. These architectures when implemented in VLSI will
reduce power consumption. Ehsan Pour Ali Akbar et al. proposed reversible signed Wallace tree multiplier in
[8]. Synthesis of reversible c i rcuits is discussed in [9]-[14] and testing of reversible circuits is discussed in [15].
1.1. Vedic Multiplication
Vedic Mathematicswas derived fro m the ancient word “Vedas”. Vedic mathematics was rediscovered in early
twentieth century. It works on the sixteen mathematical formulae called as “sutras” [16]. Mostly the speed of the
DSP processors depends mainly on the speed of its multipliers which in turn depends on number of internal log-
ics used [17]. Multipliers are used to realize many important functions such as Fast Fourier transforms and con-
S. Saravanan et al.
Figure 5 . TSG gat e as full adder.
Figure 6 . HNG gate.
Figure 7 . Quantum circu it diagram for HNG gate.
Figure 8 . HNG gate as full adder.
volutions. VLSI architectures built using these sutras will improve the performance of the system. Vedic ma-
thematics makes complex conventional calculations to be simpler and easier ones [18]. I t does the computatio ns
very fast using h uman mind. Ved ic Mathematics is a set of arithmetic rules that allo ws more efficient and spee-
dy calculatio ns. Urdh va Tirya gbhyamand Nikhilam Navatashcaramam Dashatahare the two important su-
tras involved i n multiplication . Conventionall y these Sutras are used to multiply dec imal numbers. In this pa per
these sutras were applied to binary number system which makes it compatible for digital hardware. The partial
products are generated in parallel but there will be some delay due to propagation of carry. It requires less hard-
ware to implement.
S. Saravanan et al.
1.2. Urdhva Tiryagbhyam Sutra
The Vedic Multiplier is designed using Urdh va Tiryagbhyam Sutra. This sutra has b e e n traditionally used for the
multiplication of two numbers. Urdhva Tiryagbhyam Sutra means “Vertically and Crosswise” [19]. The Least
significant bits and most significant bits are multiplied vertically. LSB and MSB bits are multiplied crosswise
and added as well. The line di agra m for Urd hva T ir yagb hya m Sutr a (step sequence from step 1 to step 7) is dis-
cussed in [3] and shown in Fig ure 9.
Tiwari et al. discussed about various Vedic Multipliers [20]. Rong Lin proposed reconfigurable and self-re-
pairable multipliers and discussed about recursive architecture decomposition of partial product matrices [21].
Deodhe et al. presented a design of 8 bit Vedic Multiplier usin g CMOS lo gic [22]. Kuma r et al. demonstrated 8
bit Vedic Multiplier usi ng ba r rel s hifte r [23]. Haghparast’s parity preserving reversible Vedic Multiplier has ad-
vantage of concurrent te s ting but its quantu m cost is high [24]. Saravanan et al. discussed about reversible Vedic
Multiplier d esign usi ng ni khilam sutra [25].
2. Proposed Reversible ALU
ALU forms the major part of any processor. In this paper a reversible ALU is designed. All components of ALU
are reversible in nature (equal inputs and outputs). Furthermore Vedic concept is adopted to enhance the speed
of the processor by reducing critical path delay. The reversible ALU consists of 8 bit Multiplier, Logical unit
and Binary to gray code converter. The sub modules are discussed below.
Figure 9 . Line diagram for Urdhva Tiryagbhyam Su tra (step sequence from step1 to step7).
S. Saravanan et al.
2.1. Vedic Multiplier
The 8 × 8 Vedic multiplier can be built fro m 2 × 2 Vedic multiplier. 8 × 8 Vedic multip lier require s 16 × 2 × 2
Vedic multiplier. 2 × 2 Vedic multiplier requires 4 multiplications and 2 half additions. To implement 8 × 8
Vedic multiplier it requires 64 multiplications and 32 half additions and 16 full additions. In contrast conven-
tional array multiplier requires 64 multiplications and 50 full adders. So hardware complexity can be reduced
using Vedic multipliers.
Consider two numbers with equal MSB and they are placed at equal distance from median value is taken. For
this case if the i np ut is t a ken in BCD form ei ght 2 × 2 Vedic multipliers and 8 bit adders are required. It requires
32 multiplications, 16 half additions and 8 full additions are required. Thus the multiplier can be implemented
with less hardware architecture.
Reversible 8 × 8 Vedic Multiplier Architecture
The multiplier architecture is shown in Figure 10. In the prop osed multiplier firs t LSB bits of multiplicand a nd
multiplier are passed on to 4 × 4 Vedic multiplier. MSB bits of multiplicand and multiplier are multiplied and
the result is once again added with MSB bits of multiplicand to get MSB of results. The algorithm works only
for multiplicand and multiplie r deviating from centra l value by equidistant.
Multipliers uses TSG gate based reversible Vedic multiplier or HNG gate based reversible Vedic multiplier.
The add er block uses 8 HNG gates. The third input of HNG gate is Carr y input. The last o utput of HNG gate is
car ry o utp ut . The four t h i np ut o f HN G ga te i s “0” i np ut. T he c ar r y o utp ut is p r o pagated to next stage carr y input
2.2. Logical Unit
It is an 8 bit logical unit. It consists of 8 peres gates. Peres gates generates AND logic and EXOR logic. The
quantum cost of Peres gate is 4. There is only one garbage output. The Reversible logic unit architecture is
shown in Fi gure 11. The inputs are A7 - A0 and B7 - B0. The input C7 - C0 is constant input which is 0. The
QQ17 - QQ10 represents logical EXOR operation. The RR17 - RR10 represents logical AND operation.
2.3. Binary to Gray Code Converter Unit
It is a n 8 b it bi nary to gra y code conver ter uni t. I t cons ists o f 8 Fe ynma n gate s. Fe ynman gates gener ate EX OR
Figure 1 0. Multiplier architecture.
S. Saravanan et al.
Figure 1 1. Reversible logic uni t architectur e.
logic . T he q uantum co st of F eyn man ga te is 1 . T her e is onl y one garbage output. The Reversible Binary to Gray
Code Converter Architecture is shown in Figure 12. T he inp uts to Fe ynma n gate ar e A7 - A0. I n this c urre nt bit
is operate d with previous bit. The Q17 - Q1 0 represents binary to gray code converted value.
2.4. Proposed Reversible ALU Archit ect ure
The ALU consists of Arithmetic unit and logic unit. The Reversible ALU architecture is shown in Figure 13.
The Reversible ALU cons ists o f 8 bit re versible Ve dic multi plie r unit, re versible lo gical unit a nd rever sible 8 bit
binary to gray code converter. The logical unit consists of Peres gate which generates AND logic and EXOR
logic. The EXOR logic is used to perform equality checking between two data.
S. Saravanan et al.
Figure 1 2. Reversible binary to gray cod e converter architectu r e.
Figure 1 3. Reversible ALU architectu re.
S. Saravanan et al.
The binary to gray code converter uses 8 Feynman gate to generate gray code. Gray codes are also called as
reflected binary codes. Since random data are generated, it may be used to generate parity bits. These parity bits
are important in error correction systems. So these codes are used in error co rrection systems, digital T V trans-
mission, etc. , these codes are used in genetic algorithms. These gray codes are used i n for ward error correction
systems. Data is transmitted over the channel. The data gets affected by noise. For a receiver in order to retrie ve
original data, it has to go for retransmission of da ta. This will consume more bandwidth. T o reduce band width
original data has to be recovered at the receiver end. This is called forward error correction. Here Reversible 8 ×
8 multip lier is designed using TSG gates and HNG gates based on Vedic concept. 8 bit logical unit is designed
using Peres gate where AND logic and EXOR logic are obtained. Peres gates are chosen because quantum cost
is 4 which is less and number of logical functions are more. 8 bit binary to gray code converter uses Feynman
gate. It gets single 8 bit input and produces corresponding output. Feynman gate is used because Quantum cost
is 1.
3. Results and Discussion
The functional si mulation of pro posed multiplier arc hitecture is simulated in Xilin x 9.2. The simulation Results
for Reversible A L U is shown in Figure 14.
The applications of this ALU are multiplication, Binary to gray code conversion, Modulo 2 operation and
Equa lity chec king. I n Figure 14 a1 corresponds to MSB of multiplicand and c1 corresponds to LSB of multip-
licand. b1 corresponds to MSB of multiplier and d1 corresponds to LSB of multiplier. h1 corresponds to MSB of
final product 06. f1 corresponds to LSB of final product 18 in hexadecimal value equivalent decimal value is 24.
qq10 - qq17 corresponds to 8 bit logical EXOR operation between A0 - A7 and B0 - B7 In the simulation results
LSB and MSB bits are interchanged. rr10 - rr17 corresponds to 8 bit logical AND operation between A0 - A7 and
B0 - B7. In the simulation results LSB and MSB bits are interchanged. q10 - q17 corresponds to 8 bit binary to
gray code value.
The system has arithmetic unit, Logical unit and binary to gray code converter. The number of functions is
The Comparison of Re versible V edic multipliers is sho wn in Table 1 . The performance of different configu-
rations of reversible 8 × 8 Vedic multipliers are analyzed and presented in Table 1 .
Figure 1 4. Simulation results for reversible ALU.
S. Saravanan et al.
Table 1. Comparison of reversible vedic multipliers [3].
Network Multiplier Type Partial
of Gates Quantum
Number of
Tot al L o g ic
Number of
Input Lines
TSG gat e 8 × 8
Vedic Multiplier Taffoli Gate 60 488 116 184a + 156b + 216d 60
TSG gat e 8 × 8
Vedic Multiplier P eres Ga t e 60 456 1 16 196a + 156b + 216d 60
TSG gat e [26]* 8 × 8
Vedic Multiplier Fredkin Gate 60 488 116 * 60
HNGGate 8 × 8
Vedic Multiplier Taffoli Gate 60 320 116 160a + 60b 60
HNGGate 8 × 8
Vedic Multiplier P eres Ga t e 60 288 1 16 192a + 60b 60
*Not given in the literature.
The quantum cost for reversible 8 × 8 Ved ic multiplier is ca lculated b y the sum of q uantum co st of two 4 × 4
reversible Vedic multiplier block and reversible adder block which can be stated mathematically as:
QC (Reversibl e 8 × 8 Ved ic multiplier) = 2*(QC of Reversible 4x4 Vedic multiplier) + (QC of adder b lock).
Among the reversible 8 × 8 Vedic multiplier configurations HNG gate with peres gate offers low quantum
cost. T he number of garb age outp uts is co nstant for a ll the cases. Among all co mbinations of multipliers, HNG
gate with T a ffoli gate partial pr oduct generation network offers low total logical calcula tions.
The number of constant input lines is same as that of number of gates required. From the table, reversible
Vedic 8 × 8 multiplier designed using HNG gate shows effectiveness in terms of quantum cost, total logic cal-
From the above table, it is found that in modern processors HNG gate based reversible Vedic multiplier ar-
chitectures may be deployed to achieve high speed.
The Comparison of Conventional multipliers and reversible logic based multipliers is shown in Table 2.
Since nu mber of logic gates needed to impleme nt adder module is le ss area will obviously be les s in reversible
The Compar ison of various 8 × 8 Multipliers based on cell u se a nd delay given b y Thapliyal in [7] is shown i n
Figure 15. All multiplier s are simulated in Xilinx platform using Virtex E XCV 300e device package, package
BG 432 and speed grade-8.
The multiplier achieves a significant improvement in performance than other multipliers. The proposed mul-
tiplier has delay of 18.8 ns (47.3% logic delay and 52.7% routing delay) whereas the delay for traditional booth
multiplier is 59 .252 ns, which justifies the red uction in multip lication. But in ter ms of cell use Tr aditional arra y
multiplier provides minimum cell use. Cell use is more for overlay booth multiplier, which indicates the area.
Cell use is optimal in reversible 8 × 8 Vedic multiplier. T he Comparison of various Multipliers ba sed on dela y is
sho wn in Figure 15.
It is found that p ropo sed reversible multiplier has less d ela y than e xi sti ng one . T he Co mpa riso n of Rever sib le
Multipliers based on delay is shown in Figure 16.
From the above d iscussion it is found that this multip lie r a rchitecture pr ovides an efficient a rithmetic unit.
It is found that Quantum cost, number of gates, garbage output and number of constant input lines are less for
pro posed logica l unit t han ex isti ng one since existi ng lo gica l unit uses P FAG ga te who se q uantu m cost i s 8 and
Feynman gate whose quantum cost is 1. The Comparison of Reversible Logic Unit based on Quantum Cost is
sho wn in Figure 17.
The quantum cost, number of gates and number of garbage output of Binary to Gray code Converter is 8 and
total logical calc ulatio n is 8 α. B ina r y to gr a y c o d e c onver ter is used in ALU since binary to gray code converter
finds its applications in error detection and cor rection and analog to digital conversio n [29] [30].
From the above all it is found that multiplier unit is operating with less delay than the existing one and has
less quantum cost. Logical unit also has less quantum cost. On a whole the ALU is efficient in terms of delay,
quantum cost, number of gates, and total logical calculations. This multiplier based ALUs can be used in
ATMEGA microcontrollers where 8 bit operation is performed [31].
S. Saravanan et al.
Figure 15. Comparison of various multipliers based on delay.
Figure 1 6. Comparison of reversible multipliers based on delay [27] .
Figure 1 7. Comparison of reversible logic unit based on quantum cost [28].
Further 2x2
Delay (ns)
Existing Multiplier [27]
Proposed 8x8 Multiplier
Delay (ns)
Reversible Multipliers
Existing Logical Unit [28]
Proposed Logical Unit
Quantum Cost
Reversible Logic Unit
S. Saravanan et al.
Table 2. Comparison of conventional multipliers and reversible logic based multipliers.
Parameters Conventional Method Reversible Logic
Num ber of gat es 88 28
Garbage outputs - 116
4. Conclusion
In summary, the proposed reversible multiplier designed using HNG gate used in ALU shows better results in
terms of dela y and quantum cost. The proposed reversible logic unit offers better performance in terms of quan-
tum cost. Hence the proposed reversible ALU as a whole performs better than the conventional method in terms
of quantum cost and delay. In advanced processor architectures there is a dedicated multiplier unit based ALU.
In future these irreversible ALU may be replaced with reversible Vedic multiplier based ALU to reduce the
quantum cost and delay. Vedic mathematics can be explored to a greater extent to optimize the various VLSI
architectures. It is presented above that when these systems are practically realized they require less number of
reve rsible gates tha n the conventional method.
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