Implementation and Comparison of Efficient 16-Bit SQRT CSLA Using Parity Preserving Reversible Gate

ISSN : 2248-9622, Vol. 6, Issue 10, ( Part -3) October 2016, pp.95-98
Rupali Patel. Int. Journal of Engineering Research and Application www.ijera.com
www.ijera.com 95 | P a g e
Implementation and Comparison of Efficient 16-Bit SQRT CSLA
Using Parity Preserving Reversible Gate
Rupali Patel*, MK Khan**
*(PG Student, VLSI and Embedded, LKCT Indore)
** (Assistant Professor, Department of Electronics and Communication, LKCT Indore)
ABSTRACT
In Very Large Scale Integration (VLSI) outlines, Carry Select Adder (CSLA) is one of the quickest adder
utilized as a part of numerous data processing processors to perform quick number crunching capacities. In this
paper we proposed the design of SQRT CSLA using parity preserving reversible gate (P2RG). Reversible logic
is emerging field in today VLSI design. In conventional circuits, the logic gates such as AND gate, OR gate is
irreversible in nature and computing with irreversible logic results in energy dissipation. This problem can be
circumvented by using reversible logic. In ideal condition, the reversible logic gate produces zero power
dissipation. The proposed design is efficient in terms of delay as compare to irreversible SQRT CSLA. The
simulation is done using Xilinx.
Keywords: Adder/Subtactor, SQRT CSLA, parity preserving gate, P2RG, reversible logic
I. INTRODUCTION
The binary addition is the fundamental
math operation in digital circuits and it got to be
crucial in a large portion of the computerized
frameworks including Arithmetic and Logic Unit
(ALU), microprocessors and Digital Signal
Processing (DSP). Outline of range and control
proficient rapid information way rationale
frameworks are a standout amongst the most
significant territories of exploration in VLSI
framework plane. In digital adder speed of addition
is restricted when required to propagate a carry
through the adder. The total addition of each and
every bit position in an elementary adder is
generated sequentially only after the previous bit
position has been summed and carry propagate into
the next position. The CSLA is utilized as a part of
numerous computational frameworks to reduce the
issue of carry propagation delay by freely producing
numerous carries and then select a carry to generate
the sum [1][2]. In fastly developing electronic
industry, faster units are of concern toward outline
as well as littler region and less power get to be real
attentiveness towards configuration of VLSI circuits.
So a VLSI optimize area, delay and power
constraints for expanding convey ability and battery
life of compact gadget.
In CMOS technology the pace of expansion
is constrained by increasing heat dissipation in
silicon chips. In VLSI circuits almost all
conventional circuits comprise million numbers of
gates (i.e. AND gate, OR gate) that are irreversible
in nature. During computation some information is
lost due to this heat dissipation and energy loss is
occurs. According to R Landauer [3], if the
manufacturing material and factor of technology is
not considered then the energy loss is only occurred
by the irreversible logical operations. The circuits
with irreversible components, during computation
each bit of information loss generates kTln2 joules
of energy, where k is Boltzmann‘s constant and T is
absolute temperature. As the heat dissipation of
circuit is increases, the performance and life of the
circuit is decreases. This problem can be overcome
by using the components which offers low power
consumption and less dissipation. According to C H
Bennet [4], we can achieve the zero energy
dissipation in the circuits if we use reversible logic
gate in place of irreversible logic components in the
circuits.
II. PARITY PRESERVING
REVERSIBLE GATE
Parity preserving is the property that will
enables the system to continue its operation properly
when failure occurs in any of the component. The
error detection and correction will be easier if the
system will be made by fault tolerance components.
Parity checking is most commonly used method for
error detection in digital logic circuits. It will most
commonly used in arithmetic and other processing
systems because those systems do not preserve the
parity of the data, there have been attempts at
performing arithmetic operations on specially
encoded operands in a way to check the parity.
These types of methods will require more
development and they are rarely used. B Parhami [5]
shown some methods of error detection in reversible
circuits, those standard methods of error detection
will present some problems because in reversible
logic circuits fan out are not allowed and we have to
take care of garbage bits. For parity preserving
RESEARCH ARTICLE OPEN ACCESS

output data, the data can be checked in manner i.e. in
a computational critical path. For parity preserving
gate the ex-or of input will matches with the ex-or of
output. For a 4*4 reversible gate it will satisfies the
condition of A ⊕B ⊕ C ⊕ D = P ⊕ Q ⊕ R ⊕ S.
Where A, B, C and D are gate inputs and P, Q, R
and S are gate outputs.
Some parity preserving reversible gates are
as follows:
Feynman Double Gate (F2G):
Fig. 1 shows 3*3 Feynman Double Gate
(F2G) [6]. It has A, B and C input vector and output
vector as P = A, Q = A⊕B, and R = A⊕C.
Fig. 1. Feynman Double Gate (F2G)
Fredkin Gate (FRG):
Fig. 2 shows 3*3 Fredkin gate (FRG) [7]. It
has A, B and C input vector and output vector as P =
A, Q= A‘B⊕ AC and R = A‘C⊕ AB.
Fig.2. Fredkin Gate (FRG)
Modified IG Gate (MIG):
Fig. 3 shows 4*4 Modified IG [8] gate. It
has A, B, C and D input vector and output vector as
P = A, Q = A⊕ B, R = AB ⊕C and S = AB‘⊕D.
Fig. 3. Modified IG Gate (MIG)
Parity Preserving Reversible Gate (P2RG):
Fig.4 shows 5*5 parity preserving
reversible gate [9], P2RG. It has A, B, C, D and E
input vector and output vector as P=A, Q=
(A‘C‘⊕B‘) ⊕D, R= (A‘C‘⊕B‘) D⊕AB⊕C,
S=AB‘⊕C⊕ (A‘C‘⊕B‘)‘D and T= (D⊕E) ⊕AC.
Fig.4. Parity Preserving Reversible Gate (P2RG)
III. IRREVERSIBLE SQRT CSLA
According to Basant Kumar [1] The square-
root carry select adder is designed by making the
delay equal via two carry chains and the multiplexer
signal from previous stage. It is also called as non-
linear carry select adder. The square-root (SQRT)
CSLA to execute huge bit-width adders with
minimum delay. In a SQRT CSLA, CSLAs with
expanding size are associated in a falling structure.
The primary goal of SQRT-CSLA outline is to
provide a parallel way for carry propagation that
decreases the in general adder. The CSLA is having
two units:
1) The sum and carry generator unit (SCG)
2) The sum and carry selection unit.
The SCG unit consumes maximum logic
resources of CSLA and mainly contributes to the
critical path. Different logic designs were suggested
for efficient implementation of the SCG unit. the
BEC based CSLA [10], made of one RCA unit and
one BEC unit as shown in fig5.
the
Fig. 2. Structure of the BEC-based CSLA; n is the
input operand bit-width.
The logical operation of n-bit RCA is
performed in four stages: 1) HSG unit, 2) FSG unit,

3) CG unit, and 4) CS unit. The logic formulas are
given in equation (1a)–(1g), and structure is shown
in Fig. 6(a). The CG unit is made of two CGs (CG0
and CG1) corresponding to input-carry ‗0‘ and ‗1‘.
The HSG receives two n-bit operands (A and B) and
generate half-sum word s0 and half-carry word c0 of
width n bits each. Both CG0 and CG1 receive s0 and
c0 from the HSG unit and generate two n-bit full-
carry words c0
1
and c1
1 corresponding to input-carry
‗0‘ and ‗1‘, respectively. The logic diagram of the
HSG unit is shown in Fig. 6(b). The optimized
designs of CG0 and CG1 are shown in Fig. 6(c) and
(d), respectively. The CS unit selects one final carry
word from the two carry words available at its input
line using the control signal cin. It selects c0
1
when
cin =0; otherwise, it selects c1
1. The CS unit can be
implemented using an n-bit 2-to-l MUX. The
optimized design of the CS unit is shown in Fig.
6(e), which is composed of n AND–OR gates. The
final carry word c is obtained from the CS unit. The
MSB of c is sent to output as cout, and (n−1) LSBs
are XORed with (n−1) MSBs of half-sum (s0) in the
FSG [shown in Fig. 6(f)] to obtain (n−1) MSBs of
final-sum (s). The LSB of s0 is XORed with cin to
obtain the LSB of s.
Fig. 6. (a) Proposed CS adder design, where n is the
input operand bit-width, and [∗] represents delay (in
the unit of inverter delay), n = max (t, 3.5n + 2.7).
(b) Gate-level design of the HSG. (c) Gate-level
optimized design of (CG0) for input-carry = 0.
(d) Gate-level optimized design of (CG1) for input-
carry = 1. (e) Gate-level design of the CS unit.
(f) Gate-level design of the final-sum generation
(FSG) unit.
IV. PROPOSED WORK
The proposed CSLA is design by using
reversible logics. The design of reversible SQRT
CSLA is same as irreversible SQRT CSLA the
difference is only that the logic gates are reversible
in nature. We used the 5*5 parity preserving
reversible gates in place of irreversible gates (AND
gate, OR gate and XOR gate). The logic
formulations are same as in equation (1a-1g). The
logic diagram for HSG unit consist n-bit parallel
adder. So we are design the parity preserving half
adder using one P2RG gate and one Fredkin gate as
shown in fig 7(a). This design has two inputs A and
B and a control line Ctrl which will control mode of
operation, i.e. when Ctrl is at logic 0, the circuit will
act as adder and when ctrl is at logic 1, the circuit
will act as subtractor. It will give three constant
inputs and four garbage bits g1 to g4. Boolean
expressions to realize the functionality of half adder
and half subtractor are given below:
Sum/Difference = A ⊕ B
Carry = A.B
Borrow = A‘. B
Fig. 7(a) Parity Preserving Full Adder/Subtractor
using P2RG gate.
The logic diagarm of AND gate using
P2RG is shown in fig 7(b). when input B= D=E=0
then output T performs AND operation i.e. (A.B).
The logic diagram of reversible OR gate is realized
using one P2RG gate and one Fredkin gate as shown
in fig 7(c). when input B=1 and D=E=0 then output
Q performs XOR operation at P2RG gate. This XOR
out is applied to the NOT gate and output of the
NOT gate performes OR operation i.e. (A+C). Not
gate is also a reversible gate because it has equal
number of input and output.
Fig.8: Reversible (a) AND Gate (b) OR Gate
V. RESULT
The 16-bit reversible SQRT CSLA is
designed using VHDL (Very High Speed Integration
Hardware Description Language). The coding is

done on Xilinx ISE 14.7 on Spartan 3 using target
device: XC3S50-PQ208 at speed grade of -5.
Simulation can be done using ModelSim SE 10.4a
simulator. The simulation results is shown in fig 9.
Fig. 9(a). Simulation result of reversible SQRT
CSLA at cin=0
Fig. 9(b). Simulation result of reversible SQRT
CSLA at cin=1
Table 1 shows the comparison of 16-bit
reversible SQRT CSLA and 16-bit irreversible
SQRT CSLA. Table 2 shows the comparative results
of parity preserving 16-bit parallel adder and 16-bit
SQRT CSLA.
Table I Comparative results of 16-bit reversible
SQRT CSLA and 16-bit irreversible SQRT CSLA
16-bit SQRT CSLA
Reversible Irreversible
LUT‘s 32 27
Slices 16 14
Bonded IOB‘s 50 50
Gate Count 188 269
Delay (ns) 14.794 17.510
Table III Comparative results of 16-bit parallel
adder and 16- bit SQRT CSLA using P2RG.
16-bit ADDER
SQRT
CSLA
Parallel
Adder
LUT‘s 32 32
Slices 16 16
Bonded IOB‘s 50 50
Gate Count 188 32
Delay (ns) 14.794 26.642
VI. CONCLUTION
This paper presents efficient way of
designing the reversible SQRT CSLA. The proposed
design demonstrates less hardware complexity and
less gate count. Gate count reduction is a sign of
area reduction. The proposed 16-bit SQRT CSLA
offers less gate count and delay as compare to
irreversible SQRT CSLA. When it is compare with
the 16-bit parallel adder using P2RG it offers less
delay but gate count is increases. For future to
explore in this work is to design more optimized
fault tolerant adder and other fault tolerant circuits in
a way to reduce the area power and delay.
REFERENCES
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[3]. R. Landauer, ―Irreversibility and heat
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Implementation and Comparison of Efficient 16-Bit SQRT CSLA Using Parity Preserving Reversible Gate

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