Implementation of an Effective Self-Timed Multiplier for Single Precision Floating Values with Carry-Look Ahead Adder

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 530
Implementation of an Effective Self-Timed Multiplier for Single
Precision Floating Values with Carry-Look Ahead Adder
Shradda Awate1, Veerabhadrappa S.T2
1M.Tech Student, Department of Electronics and Communication, VLSI Design and Embedded Systems, JSS
Academy for Technical Education, Bengaluru, India.
2Associate Professor, Department of Electronics and Communication, JSS Academy for Technical Education,
Bengaluru, India.
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Abstract - The digital signals are represented also in the
form of floating point values. Processing of data or signal
involves the mathematicaloperationstogetthedesiredoutput
of the system. This paper presents a self-timed multiplier for
32-bit floating point values with carrylookaheadadderbased
on IEEE754 standards using VHDL, implemented on Spartan-
3E FPGA Board.
Key Words: Floating point multiplier, IEEE754 floating-
point representation, carry look ahead adder, VHDL,
FPGA.
1. INTRODUCTION
In a wide range of the DSP application, FIR filter,andsoforth
need floating point number arithmetic [1]. Floating point
representation is thepossiblewaytorepresent real numbers
on computer. Multiplications of the floating point values are
useful in applications where a substantial dynamic range is
required. The floating point multiplier helps to multiply two
single precision floating point values on FPGA Spartan-3E
board based on IEEE 754 standards.
The real numbers on UNIX, Linux, Mac and windows are
represented using IEEE754 standardsfloatingpoint number
representation [2]. The self-timed multiplier for 32-bit
floating point consists of multiplexer, adder, shifter,
normalize and subtract units. Salty Beohara et al say’s that
designing the floating multiplier block with synchronous
logic has many disadvantages such as latency is more,
throughput is less, higher power consumptionsandcomplex
clock distribution network [2]. These disadvantages are
overcome by using the asynchronous approach. In
asynchronous method, there is no necessity for clock
synchronization. The self-timed multiplier works in all the
environmental and operating conditions. Fu-Chiung et all
demonstrated a self-timed multiplier is much more faster
than the multiplier built using synchronous logic [3]. Since
this asynchronous approach render solutions to all these
problems, hence will do the asynchronouslogictomakeself-
timed multiplier in this paper.
2. IEEE FLOATING POINT REPRESENTATION
The floating point representation in computer is first
introduced by IEEE in 1985. According to the Michael L.
Overton floating Point Representation method is used to
store real number on computer [4]. The floating point
numbers are represented by using single precision format
(32-bit floating number)and doubleprecisionformat(64-bit
floating number).
Single Precision floating point format is of 32-bitsand it is
composed of three fields, such as sign field, exponent field
and mantissa field [4]. 1 bit is assigned forsignfield,8binary
bits are assigned for exponent field and 23 binary bits are
assigned for mantissa field.
Sign Bit: - sign of the number depends on the sign bit.. If the
sign bit is 1, the floating point number is negative and else is
positive[4].
Exponent Field: - This field is used to represent absolute
value of integer exponents. To find out thestored exponenta
bias value is summed with the exponent. Bias value for
exponent of single precision is 127 and the bias value for
exponent of double precision is 1023.
Mantissa Field: - Mantissa is also called as significant which
represents the precision bits of the real number. Binary “1”
is appended to mantissa in this representation.
Figure 1 shows the single precision floating point format.
Figure 1: IEEE single precision floating point format
IEEE single precision floatingpoint numberisrepresentedin
this format as follows,
X = (-1)S * 2(E –Bias) * (1.M) (1)
Where
M = b222-1 + b212-2 + ................+ b12-22 + b02-23 (2)
Bias for 32-bit floating point number = 2(8-1) - 1 = 127.
And S can be 1 or 0 depending on number.

As similar to single precision floating point numbers,double
precision floating point numbers also consists of the three
fields, they are sign field, exponent field and mantissa field
[4]. 1 bit is assigned for sign field, 11binary bits are assigned
for exponent field and 52 binary bits are assigned for
mantissa field.
Figure 2 shows the double precision floating point format.
Figure 2: IEEE double precision floating point format
IEEE double precision floating point number is represented
in this format as follows,
Bias for 32-bit floating point number = 2(10) - 1 = 1023.
3. MULTIPLICATION OF TWO FLOATING VALUES
The following steps are applied to multiply single
precision floating point numbers.
1) Convert decimal value to its appropriate binary.
2) Converting binary representation of two operands
to standard floating format.
3) Identifying the sign bit of the result by XOR-ing the
sign bits of operands.
4) Multiplying the mantissa fieldsofboththeoperands
along with the hidden ‘1’.
5) Sum of the exponents of both the operands is
computed and then subtracted with the bias value.
Figure 3 shows the basic block diagram of the floating point
multiplier.
Figure 3: floating point multiplier.
Demonstration of multiplication of two 32-bit floating point
numbers based on IEEE 754 standard using the above steps.
A = 6.25 and B = 585.25
1) Binary Representation of above two operands are,
A = 110.01
B = 1001001001.01
2) IEEE 754 single precision representation of the operands
A = 01000000110010000000000000000000
B = 01000100000100100101000000000000
3) Two sign bits of multiplier and multiplicand are XOR’d to
get the resultant sign bit. Hence in this case sign bit of
result is 0.
4) Mantissa multiplication yields resultant mantissa bits
after normalizing it. In this case final output mantissa is,
11001001001110100000000.
5) Now exponent bits are found out by addition and
subtraction operations. Therefore, final result of
multiplication in IEEE 754 standard is as shown in
Figure 4.
0 10001010 11001001001110100000000
Figure 4: Result of multiplication.
AxB = 6.25 x 585.5 = 111001001001.1101 = 657.8125
Flowchart for the floating point numbers multiplication is
shown in figure 5,
Figure 5: Flowchart

4. METHODOLOGY
The resultant exponent is obtained by simply adding
operation which is done by using a single asynchronous
carry look ahead adder. The carry-look-ahead adder also
termed as fast adder is used in this multiplier. The entire
operation of the system becomes self-timed as self-timed
CLA is used to build the self-timed multiplier. The proposed
multiplier is termed asself-timedmultiplierbecausetheself-
timed carry-look-ahead adder is used in this paper.
In order to perform addition operation of two binary
exponent bits of two floating valuesa singlecarrylook ahead
adder is used. The reason behind using this fast adder isthat
the addition process is faster than that in ripple carry adder.
In carry-look-ahead adder carry signalsofsubsequentadder
stages are computed faster. The carry bit inself-timedcarry-
look-ahead adder is computed by using the input bits.
Figure 6: Structure of 4-bit carry look ahead adder
Carry look-ahead adders structure is as shown in the Figure
6. It consists of mainly three blocks namely,
Propagate/generate generator, Sum generator and carry
generator
The general expression of the carry look ahead adder is as
follows,
PI = AI * BI Carry propagate (3)
GI = AI * BI Carry generate (4)
SI = PI * CI-1 output sum (5)
CI+1 = GI + PI * CI carryout (6)
From above expressions, it is clear that present carry-in
doesn’t depend on its previous carry-out. Hence the general
expression for carry is,
CI+1= GI + PI GI-1 + PIPI-1GI-2 + .......+ P1P0C0 (7)
5. RESULTS AND DISCUSSIONS
Figure 7 shows the block diagramoftheself-timedmultiplier
for two 32-bit floating point numbers using VHDL.
Subsequent operations are performed to get the output of
the multiplication process which involvesvariousstepssuch
as normalizing, addition, subtracting, multiplying, XOR
operation.
The VHDL code for the self-timed multiplier is synthesized
and simulated by utilizing Xilinx ISE 14.4 software. The
Xilinx tool is used to design circuit based on the users
description and enables to simulate, place and route.
FPGA Spartan-3A board is used to executetheVHDLcode for
self-timed floating point multiplier. The code is downloaded
from host to the Spartan-3A board via USB port. Field
programmable gate array (FPGA) is used to debug the VHDL
code.
Table - I shows the results of the various two 32-bit floating
point number multiplier. Figure 8 shows the sample input
and output waveforms for the multiplication of numbers
445.65 and 745.78. The proposed self-timed multiplier
achieves better precision. The precision of the self-timed
multiplier is good as compared to multiplying 8-bits of
floating point multiplier.
Figure 7: The block diagram of the overall project.

Table -1: Multiplier output
A B Output
5.25 286.75 1505.4375
6.25 585.25 3657.8125
23 12 276
44 5 220
9 5 45
Figure 8: Input and output waveforms
6. CONCLUSION AND FUTURE SCOPE
The Simulation result demonstratesthatmultiplierwithself-
timed Carry Look Ahead adder successfully multiplies two
single precision floating values. The self-timed multiplier
works correctly under normal, overflow and underflow
conditions. In future this self-timed multiplier can be
extended for multiplying two 64-bit floating point data
format. The self-timed multiplier can also be built for
multiplying more than two floating point number system.
ACKNOWLEDGEMENT
The authors would like to thank JSS Academy for Technical
Education, Bengaluru for providing an opportunity to learn
and work on a project at Cranes Varsity Pvt. Ltd.
REFERENCES
1. Karthik.S, Sunilkumar B.S “Implementation of
Floating Point Multiplier Using Dadda Algorithm”
International Journal of Electrical, Electronics and
Computer Systems (IJEECS).
2. Salty Beohara and Sandip Nemade “VHDL
Implementation of Self-Timed 32-Bit FloatingPoint
Multiplier with Carry Look Ahead Adder”.
Electronics and Communication Engineering,
Technocrats Institute of Technology (TIT) Bhopal,
India.
3. Fu-Chiung Cheng Stephen H. Unger Michael
TheobaldWen-ChungCho“Delay-InsensitiveCarry-
Look ahead Adders”, VLSI Design, 1997.
Proceedings. Tenth International Conferenceon4-7
Jan 1997.
4. Michael L. Overton “Floating Point Representation”,
http://homepage.cs.uiowa.edu/~atkinson/m170.di
r/overton.pdf
5. Omid Sarbishei and Katarzyna Radecka “On the
Fixed-Point Accuracy Analysis and Optimization of
FFT Units withCORDICMultipliers”,201120thIEEE
Symposium on Computer Arithmetic

Implementation of an Effective Self-Timed Multiplier for Single Precision Floating Values with Carry-Look Ahead Adder

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Implementation of an Effective Self-Timed Multiplier for Single Precision Floating Values with Carry-Look Ahead Adder