Braun’s Multiplier Implementation using FPGA with Bypassing Techniques.

International Journal of VLSI design & Communication Systems (VLSICS) Vol.2, No.3, September 2011
DOI : 10.5121/vlsic.2011.2317 201
Braun’s Multiplier Implementation using
FPGA with Bypassing Techniques.
Anitha R1
, Bagyaveereswaran V2
1
VIT University, Vellore, India.
eranitharavi@gmail.com
2
VIT University, Vellore, India.
vbagyaveereswaran@vit.ac.in
Abstract:
The developing an Application Specific Integrated Circuits (ASICs) will cost very high, the circuits should
be proved and then it would be optimized before implementation. Multiplication which is the basic building
block for several DSP processors, Image processing and many other. The Braun multipliers can easily be
implemented using Field Programmable Gate Array (FPGA) devices. This research presented the
comparative study of Spartan-3E, Virtex-4, Virtex-5 and Virtex-6 Low Power FPGA devices. The
implementation of Braun multipliers and its bypassing techniques is done using Verilog HDL. We are
proposing that adder block which we implemented our design (fast addition) and we compared the results
of that so that our proposed method is effective when compare to the conventional design. There is the
reduction in the resources like delay LUTs, number of slices used. Results are showed and it is verified
using the Spartan-3E, Virtex-4 and Virtex-5 devices. The Virtex-5 FPGA has shown the good performance
as compared to Spartan-3E and Virtex-4 FPGA devices.
Key words:
Digital Signal Processing (DSP), Field Programmable Gate Array (FPGA), fast addition, Spartan-3E,
truncated multiplier, Verilog HDL, Virtex-4, Virtex-5, Virtex – 6 Low power.
1. INTRODUCTION
Multiplication – an important fundamental function in arithmetic operation. Currently
implemented in many DSP applications such as FFT, Filtering etc., and usually contribute
significantly to time delay and take up a great deal of silicon area in DSP system. Now – a – days
time is still an important issue for the determination of the instruction cycle time of the DSP chip.
Both the multiplication and the DSP play a vital role in the implementation of VLSI system.
Multiplication – Repeated addition of n – bits will give the solution for the multiplication. ie.
Multi-operand addition process. The multi – operand addition process needs two n – bit operands.
It can be realized in n- cycles of shifting and adding. This can be performed by using parallel or
serial methods. This will be simple to implement in two’s complement representation, since they
are independent of the signs. It is advantageous to exploit other number systems to improve speed
and reduce the chip area and power consumption.

202
Generally multiplications can be carried out in all the types of number system. The one which
carried out for the Binary number system is the Digital Multiplier.
A Field-programmable Gate Array (FPGA) is an integrated circuit designed to be configured
by the customer or designer after manufacturing. Field Programmable means that the FPGA's
function is defined by a user's program rather than by the manufacturer of the device. A typical
integrated circuit performs a particular function defined at the time of manufacture. In contrast,
the FPGA's function is defined by a program written by someone other than the device
manufacturer. Depending on the particular device, the program is either 'burned' in permanently
or semi-permanently as part of a board assembly process, or is loaded from an external memory
each time the device is powered up. This user programmability gives the user access to complex
integrated designs without the high engineering costs associated with application specific
integrated circuits (ASIC).
2. BRAUN MULTIPLIERS:
It is a simple parallel multiplier generally called as carry save array multiplier. It has been
restricted to perform signed bits. The structure consists of array of AND gates and adders
arranged in the iterative manner and no need of logic registers. This can be called as non –
addictive multipliers. Architecture:
An n*n bit Braun multiplier [9] & [10] is constructed with n (n-1) adders and n2
AND gates as
shown in the fig.1, where,
The internal structure of the full adder can be realized using FPGA. Each products can be
generated in parallel with the AND gates. Each partial product can be added with the sum of
partial product which has previously produced by using the row of adders. The carry out will be
shifted one bit to the left or right and then it will be added to the sum which is generated by the
first adder and the newly generated partial product.

203
The shifting would carry out with the help of Carry Save Adder (CSA) and the Ripple carry adder
should be used for the final stage of the output. Braun multiplier performs well for the unsigned
operands that are less than 16 bits in terms of speed, power and area. But it is simple structure
when compared to the other multipliers. The main drawback of this multiplier is that the potential
susceptibility of Glitching problem due to the Ripple Carry Adder in the last stage. The delay
depends on the delay of the Full Adder and also a final adder in the last. The power and area can
also be reduced by using two bypassing techniques called Row bypassing technique (fig. 2) [4
& 3] and Column bypassing technique (fig. 3) [4].
Fig. 2 4*4 row bypassing

204
Fig. 3 4*4 column bypassing
In this paper we have simulated and synthesized the Braun’s multiplier and the bypassing
multipliers (row bypassing and column bypassing) and then we compare the results of the
multipliers. The objective of this study is to present a comparative study of Braun’s multiplier and
bypassing technique using Spartan-3E, Virtex-4, Virtex-5 and Virtex 6 low power FPGA devices.
3. PROPOSED METHOD:
The Braun’s Multiplier (fig. 1) which uses the full adder block adding the PP. in the proposed
method we have used the fast addition [9] method so that we are reducing the number of slices,
LUTs, and the delay is getting reduced. The fig. 4 which shows the proposed method of the
Braun’s multiplier.
In the proposed method the number of LUTs, slices are reduced and mainly the delay has been
very less when compare to the conventional method. The table.1 will give the comparison result
of the all the methods which is simulated and synthesized and tested in the FPGA boards.
The Row bypassing and the Column bypassing method also simulated and synthesized by using
the proposed method. Table 1 will show the result of those multipliers.
3a. TWO DIMENSION BYPASSING TECHNIQUE:
Fig 4. 4x4 2D Bypassing Multiplier in Braun Multiplier fig. 5. Adder cell

205
The modified Adder cell in two-dimensional bypassing Fig.4. consists of a FA, 3 tri-state buffers,
two 2-to-1 mux and an extra AND gate at the carry output of the FA as shown in Fig.5. To correct
the carry propagation in the multiplication result, the addition operations in the (i+1)th
column or
the jth
row cannot be bypassed if the bit ai is 0, the bit bj is 0, and the carry bit, ci,j-1, is 1. Hence,
the bypass logics are added into the necessary FA to form a correct adder cell (AC).
3b.ROW AND COLUMN BYPASSING TECHNIQUE
Fig. 6. Column and row bypassing multiplier
The carry bit in the (i+1, j)th
FA can be replaced by the AND operation of the product, aibj and the
carry bit ci,j-1. For the addition operation in FA, the (i+1, j)th
FA, 1 < j < n, can be replaced with the
modified half adder, A+B+1(Fig.6(c)) and the HAs in the first row of CSAs can be replaced with
the incremental adder, A+1(Fig.6(a)). Based on the operation simplification of full adders in an
array multiplier, a low-power multiplier with row and column bypassing can be obtained.Besides
that, each simplified adder, A+1, in the CSA array is only attached by one tri-state buffer and two
2-to-1 multiplexers and each simplified adder, A+B+1, in the CSA array is only attached by two
tri-state buffers and two 2-to-1 multiplexers.
Fig.6 (a) A+1 Adder (b) A+B Adder (c) A+B+1 Adder

206
Fig.7 Row & Column Bypassing Adder Cell.
4. IMPLEMENTATION USING SPARTAN 3E, VIRTEX 4, VIRTEX 5
AND VIRTEX 6 Low Power FPGA DEVICES [11]:
4.1 FPGA design and implementation results: The design of standard, row bypassing, column
bypassing and the proposed 4×4 multipliers are simulated and synthesis using Verilog HDL and
implemented in the Xilinx Spartan – 3E (xc3s500e-4ft256), Virtex – 4 (xc4vlx15-10-sf363),
Virtex – 5 (xc5vlx30-1-ff324), and Virtex – 6 ((xc6vlx75tl-1L-ff484) FPGAs using the Xilinx
ISE 12.4 design tool and as well as simulated using the Design Architect tool of Mentor
Graphics.
Table 1: FPGA resource utilization for standard, row and column bypassing and proposed 4*4
multiplier for Spartan-3E (xc3s500e-4ft256)

207
multiplier for Virtex – 4(xc4vlx15-10-sf363)
multiplier for Virtex – 5(xc5vlx30-1-ff324)

208
multiplier for Virtex – 6 Low power (xc6vlx75tl-1L-ff484)
Fig. 8 The LUTs for Spartan-3AN, Virtex-4, Virtex - 5 and Virtex-6 for standard, row and
column bypassing and proposed 4*4 Braun’s multipliers

209
Fig. 9 The Slices for Spartan-3AN, Virtex-4, Virtex - 5 and Virtex-6 for standard, row and
column bypassing and proposed 4*4 Braun’s multipliers
Fig. 10 The bonded IOBs for Spartan-3AN, Virtex-4, Virtex - 5 and Virtex-6 for standard, row
and column bypassing and proposed 4*4 Braun’s multipliers

210
Fig. 11 The combinational path delay for Spartan-3AN, Virtex-4, Virtex - 5 and Virtex-6 for
standard, row and column bypassing and proposed 4*4 Braun’s multipliers
Fig. 12 The average pin delay for Spartan-3AN, Virtex-4, Virtex - 5 and Virtex-6 for standard,
row and column bypassing and proposed 4*4 Braun’s multipliers

211
Table 1-4 summarize the FPGA devices resources utilization for standard, row and column
bypassing and proposed 4*4 Braun’s multipliers
Figure 8 shows the comparison of number of LUTs for Spartan-3E, Virtex-4, Virtex - 5 and
Virtex-6 FPGA devices for standard, row and column bypassing and proposed 4*4 Braun’s
multipliers, which clearly indicates that the virtex-6 FPGA device utilizes fewer resources than
Spartan-3E, Virtex-4, and Virtex - 5 devices.
The number of slices and the bonded IOBs are compared in the fig. 9 and fig.10, the figure
clearly shows that Virtex 6 has the less percentage of among all the FPGAs.
The table 1 -4 is showing the comparison result of the total combinational path delay of the
multipliers and the graph has been plotted as shown in the fig. 11. It shows that Virtex -6 showing
the less delay so that speed of the multiplier can increase. And the fig. 12 showing that the
average timing delay between the pins which is used in the multipliers.
5.CONCLUSION
In this paper we have presented the hardware implementation of the Multipliers in the FPGA
devices using Verilog HDL. The design was implemented on the Xilinx Spartan – 3E (xc3s500e-
4ft256), Virtex – 4 (xc4vlx15-10-sf363), Virtex – 5 (xc5vlx30-1-ff324), and Virtex – 6
((xc6vlx75tl-1L-ff484) FPGAs. The proposed Multiplier shows that reduced utilization when
compare to all other multipliers. The average pin delay and combinational path delay has been
reduced in the Virtex – 6 Low power FPGA device. So the Virtex – 6 Low power is obtained the
best result when compare to the other FPGA devices. And it is feasible for the DSP Processor,
Image processing and multimedia technology.
6.FUTURE WORK
Braun Multiplier can be modified using the adder cell, which can be replaced with the Kogge
Stone adder/non linear carry select adder can be designed using the RTL complier where we can
draw the layout and then validation can also be done.
REFERENCE
[1] Muhammad H. Rais, “Hardware Implementation of Truncated Multipliers Using Spartan-3AN,
Virtex-4 and Virtex-5 FPGA Devices”, Am. J. Engg. & Applied Sci., 3 (1): 201-206, 2010.
[2] M.A. Ashour*, H.I. Saleh, “An FPGA implementation guide for some different types of serial–
parallel multiplier structures”, Microelectronics Journal 31 (2000) 161–168.
[3] J. T. Yan and Z. W. Chen, “Low-power multiplier design with row and column bypassing,” IEEE
International SOC Conference, pp.227-230, 2009.
[4] J. T. Yan and Z. W. Chen,” Low-Cost Low- Power Bypassing-Based Multiplier Design,”IEEE 2010.

212
[5] M. C. Wen, S. J. Wang and Y. M. Lin, “Low power parallel multiplier with column bypassing,“ IEEE
International Symposium on Circuits and Systems, pp.1638-1641, 2005.
[6] Sanjiv Kumar Mangal, Rahul M. Badghare, Raghavendra B. Deshmukh, R. M. Patrikar,”FPGA
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[7] Yin-Tsung Hwang , Jin-Fa Lin , Ming-Hwa Sheu and Chia-Jen Sheu,” Low Power Multipliers Using
Enhenced Row Bypassing Schemes”, IEEE 2007.
[8] Neil H.E.Weste, David Harris, Ayan Banerjee, “CMOS VLSI Design, A circuits and system
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[9] Kiat – Seng Yeo and Kaushik Roy,” Low Voltage, Low Power VLSI Subsystems”, TMC 2009 ed.
[10] Lars Wanhannar,” DSP Integrated Circuits”, Academic Press.
[11] www.xilinx.com
[12] Chen,Kungching, ”Types of adders”, M. Eng. Project_ 2005.

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