Design of high speed area optimized binary coded
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The document presents a design for a high-speed, area-optimized binary-coded decimal (BCD) digit adder aimed at improving decimal arithmetic used in various applications like banking and billing, addressing the issues of delay and area requirement. The proposed adder eliminates the need for correction values by implementing a correction-free mechanism, thus enhancing performance. The design, simulated using Verilog, demonstrates significant improvements in efficiency over existing systems requiring additional correction circuits.
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 374
DESIGN OF HIGH SPEED AREA OPTIMIZED BINARY CODED
DECIMAL DIGIT ADDER
Deepak Rao1
, Anuradha2
1
Department of ECE, VLSI Design & Embedded System, Appa Institute of Engineering &Technology, Gulbarga
2
Department of ECE, VLSI Design & Embedded System, Appa Institute of Engineering & Technology, Gulbarga
Abstract
Decimal arithmetic is necessary for computations in the field of banking systems,tax calculations,telephone billings etc. The main
problem in the prevailing decimal arithmetic is the requirement of the correction of the result in its binary form. This results in larger
area and implementation delay. The proposed adder is improved for less delay and area requirement as a correction free mechanism
provides the result without adding any correction values.
Keywords:BCD Adder, Verilog code, Xilinx 9.2i.
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1. INTRODUCTION
Inthe era of electronic computing, decimal arithmetic plays a
vital role in commercial, financial, internet and industrial
control applications. Most of the computing applications are
based on binary arithmetic, but the real problem is that binary
approximation does not produce accurate result. For example if
a telecommunication company approximates a 5% sale tax on
an. Binary decimal arithmetic is required to avoid such
incorrect approximations. Also, in most of the applications,
decimal software runs on custom binary hardware in order to
produce precise decimal results, leading to another problem of
excessive delays. Software implementation of decimal
arithmetic is about 100 to 1000 times slower than the binary
implementation in hardware. In a survey of IBM corporation
showed that almost 55% of the numeric data columns, used by
51 major organization’s databases, were decimal data types and
43.7% were integer types which can be stored as decimals. In
order to meet the need for growing evolution of decimal
arithmetic, it’s necessary to develop efficient
algorithms.Decimal digit adders and decimal digitmultipliers
are the building blocks of anydecimal hardware to support
decimalarithmetic.Here is a proposed high speed and area
optimized decimal digit adder. The design is described and
simulated using verilog hardware description language.
2. LITERATURE SURVEY
A combined binary and decimal adder was introduced by
I.S.Hwang[3]. The binary carry look ahead adder adds two
input operands which are either binary or decimal. Also a
reduced delay bcd adder with improved delay was proposed by
AlpArslaBayrakci and Ahmet Akkas[1]. Here a parallel prefix
network was used to generate carry thereby reducing the delay
in multi digit addition. Decimal Multiplication via carry-save
addition was introduced by Mark A.Erle and Michael
J.Schulte[5] where carry save addition was used to reduce
critical path delay.
3. PROPOSED BCD ADDER
Here an optimized correction free BCD digit adder is proposed.
The 2 decimal input digits of the BCD adder are A€ {0, 9} and
B€ {0, 9} and the decimal carry input is Cin. We can represent
the decimal sum and the decimal carry as as S€ {0, 9} and Cout
respectively. The decimal value of A, B, and S can be used to
obtain their 8421 BCD representation. In general, we can write
A =a3a2a1a0, B = b3b2b1b0, and S =s3s2s1s0, where ai, bi, and si €
{0, 1} i € {0, 1, 2, 3}. A and B can be expressed in terms of
two integers m = a3a2a1and n = b3b2b1as:
A = 2 × m+ a0and B = 2 × n + b0, where 0 ≤ m ≤ 4 and 0 ≤ n
≤4.This implies that the output of the BCD adder can be
expressed as
{COUT, SUM} = A+B+CIN
We can rearrange the above expression for BCD adder output
as:
{COUT,SUM} = (2 x m + a0) + (2 x n + b0) + Cin
=(2 x n +m) + (a0+b0+Cin)
Using the above formula, BCD digit adder is designed that
consists of two stages: Stage1 and Stage2. The inputs to Stage1
are m and n. Stage1 generates the partial decimal sum: Z =
z3z2z1z00 = 2 × (n + m). It should be observed that this decimal
partial sum consists of an even decimal digit (z2z1z0 0) and a
decimal carry z3 that can be either 1 or 0 based on the values of
m and n.](https://image.slidesharecdn.com/designofhighspeedareaoptimizedbinarycoded-140821055407-phpapp01/85/Design-of-high-speed-area-optimized-binary-coded-1-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 375
4. BLOCK DIAGRAM.
This block diagram consists of two stages wherein the first
stage computes the n and m values from the given input values.
Stage 1 generatespartial decimal sum Z = Z0Z1Z2Z3 =2 x (n +
m). This partial sum consists of even decimal digit z2z1z00
and a decimal carry z3 based on m & n. The second stage
generates the required sum. Since result of stage1 is always
even, only z2z1z00 are passed to stage2. The outputs of Stage1
along with a0, b0, and Cin are given as input to Stage2. In order
to design Stage2, the values of Cout, s3, s2, s1, and s0 are
calculated for all possible combinations of z3, z2, z1, z0, a0, b0,
and Cin and optimized boolean equations for Stage2 are
derived.
Fig 1Block Diagram of proposed Adder
5. SIMULATION RESULTS
Fig 2 Simulation result of correction free BCD Adder
Fig 3 Design Summary
Figure 2 here shows the simulation result of the proposed BCD
adder. Two decimal numbers less than 9 are added. Figure 3
shows the device utilization summary iwhich shows the number
of LUT’s required, number of slices and number of IOB,s
sequentially.
6. CONCLUSIONS
In this report, direct Boolean expression binary coded decimal
digit adder will produce the output in the BCD form. As a result
a correction free BCD digit adder is obtained when compared
with the existing system which needs an analyzer circuit for
determining the whether the output value is greater than 9.Here
the Boolean expression is obtained using two-level logic
optimization is modified to multilevel logic optimization for
reducing the area and delay. The design is synthesized, verified
and tested for correct functionality using verilog coding and
simulation.
REFERENCES
[1].Alp ArslanBayrakci and Ahmed Akkas “Reduced Delay
BCD Adder” IEEE International Conf. on Apllication –specific
Systems, Architectures and Processors (ASAP 2007). Volume-
Issue: 9-11,Page(s):266-271 July2007
[2]. A.Vazquez,E. Antelo, “Conditional speculative decimal
addition, “Nancy,France,2006, pp. 47-57.
[3]. I.S. Hwang, ”High Speed Binary and Decimal Arithmetic
Unit”, United States Patent 2007.
[4]. Osama Al-Khaleel,Mohammad Al-Khaleel, Zakariah Al-
Qudah “Fast Binary/Decimal Adder/Subtracter with a novel
correction free BCD Addition” in IEEE Cinferece on Computer
arithmetic, 2011.
[5].M.A.Erleand M.J.Shulte “Decimal Multiplication via Carry-
Save Addition” (June 2003) IEEE lnt’l Conference on
Application Specific system Architectures and Processors, pp
.348-358.](https://image.slidesharecdn.com/designofhighspeedareaoptimizedbinarycoded-140821055407-phpapp01/85/Design-of-high-speed-area-optimized-binary-coded-2-320.jpg)
Design of high speed area optimized binary coded
- 1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 374 DESIGN OF HIGH SPEED AREA OPTIMIZED BINARY CODED DECIMAL DIGIT ADDER Deepak Rao1 , Anuradha2 1 Department of ECE, VLSI Design & Embedded System, Appa Institute of Engineering &Technology, Gulbarga 2 Department of ECE, VLSI Design & Embedded System, Appa Institute of Engineering & Technology, Gulbarga Abstract Decimal arithmetic is necessary for computations in the field of banking systems,tax calculations,telephone billings etc. The main problem in the prevailing decimal arithmetic is the requirement of the correction of the result in its binary form. This results in larger area and implementation delay. The proposed adder is improved for less delay and area requirement as a correction free mechanism provides the result without adding any correction values. Keywords:BCD Adder, Verilog code, Xilinx 9.2i. -------------------------------------------------------------------------***----------------------------------------------------------------- 1. INTRODUCTION Inthe era of electronic computing, decimal arithmetic plays a vital role in commercial, financial, internet and industrial control applications. Most of the computing applications are based on binary arithmetic, but the real problem is that binary approximation does not produce accurate result. For example if a telecommunication company approximates a 5% sale tax on an. Binary decimal arithmetic is required to avoid such incorrect approximations. Also, in most of the applications, decimal software runs on custom binary hardware in order to produce precise decimal results, leading to another problem of excessive delays. Software implementation of decimal arithmetic is about 100 to 1000 times slower than the binary implementation in hardware. In a survey of IBM corporation showed that almost 55% of the numeric data columns, used by 51 major organization’s databases, were decimal data types and 43.7% were integer types which can be stored as decimals. In order to meet the need for growing evolution of decimal arithmetic, it’s necessary to develop efficient algorithms.Decimal digit adders and decimal digitmultipliers are the building blocks of anydecimal hardware to support decimalarithmetic.Here is a proposed high speed and area optimized decimal digit adder. The design is described and simulated using verilog hardware description language. 2. LITERATURE SURVEY A combined binary and decimal adder was introduced by I.S.Hwang[3]. The binary carry look ahead adder adds two input operands which are either binary or decimal. Also a reduced delay bcd adder with improved delay was proposed by AlpArslaBayrakci and Ahmet Akkas[1]. Here a parallel prefix network was used to generate carry thereby reducing the delay in multi digit addition. Decimal Multiplication via carry-save addition was introduced by Mark A.Erle and Michael J.Schulte[5] where carry save addition was used to reduce critical path delay. 3. PROPOSED BCD ADDER Here an optimized correction free BCD digit adder is proposed. The 2 decimal input digits of the BCD adder are A€ {0, 9} and B€ {0, 9} and the decimal carry input is Cin. We can represent the decimal sum and the decimal carry as as S€ {0, 9} and Cout respectively. The decimal value of A, B, and S can be used to obtain their 8421 BCD representation. In general, we can write A =a3a2a1a0, B = b3b2b1b0, and S =s3s2s1s0, where ai, bi, and si € {0, 1} i € {0, 1, 2, 3}. A and B can be expressed in terms of two integers m = a3a2a1and n = b3b2b1as: A = 2 × m+ a0and B = 2 × n + b0, where 0 ≤ m ≤ 4 and 0 ≤ n ≤4.This implies that the output of the BCD adder can be expressed as {COUT, SUM} = A+B+CIN We can rearrange the above expression for BCD adder output as: {COUT,SUM} = (2 x m + a0) + (2 x n + b0) + Cin =(2 x n +m) + (a0+b0+Cin) Using the above formula, BCD digit adder is designed that consists of two stages: Stage1 and Stage2. The inputs to Stage1 are m and n. Stage1 generates the partial decimal sum: Z = z3z2z1z00 = 2 × (n + m). It should be observed that this decimal partial sum consists of an even decimal digit (z2z1z0 0) and a decimal carry z3 that can be either 1 or 0 based on the values of m and n.
- 2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308 __________________________________________________________________________________________ Volume: 03 Special Issue: 03 | May-2014 | NCRIET-2014, Available @ http://www.ijret.org 375 4. BLOCK DIAGRAM. This block diagram consists of two stages wherein the first stage computes the n and m values from the given input values. Stage 1 generatespartial decimal sum Z = Z0Z1Z2Z3 =2 x (n + m). This partial sum consists of even decimal digit z2z1z00 and a decimal carry z3 based on m & n. The second stage generates the required sum. Since result of stage1 is always even, only z2z1z00 are passed to stage2. The outputs of Stage1 along with a0, b0, and Cin are given as input to Stage2. In order to design Stage2, the values of Cout, s3, s2, s1, and s0 are calculated for all possible combinations of z3, z2, z1, z0, a0, b0, and Cin and optimized boolean equations for Stage2 are derived. Fig 1Block Diagram of proposed Adder 5. SIMULATION RESULTS Fig 2 Simulation result of correction free BCD Adder Fig 3 Design Summary Figure 2 here shows the simulation result of the proposed BCD adder. Two decimal numbers less than 9 are added. Figure 3 shows the device utilization summary iwhich shows the number of LUT’s required, number of slices and number of IOB,s sequentially. 6. CONCLUSIONS In this report, direct Boolean expression binary coded decimal digit adder will produce the output in the BCD form. As a result a correction free BCD digit adder is obtained when compared with the existing system which needs an analyzer circuit for determining the whether the output value is greater than 9.Here the Boolean expression is obtained using two-level logic optimization is modified to multilevel logic optimization for reducing the area and delay. The design is synthesized, verified and tested for correct functionality using verilog coding and simulation. REFERENCES [1].Alp ArslanBayrakci and Ahmed Akkas “Reduced Delay BCD Adder” IEEE International Conf. on Apllication –specific Systems, Architectures and Processors (ASAP 2007). Volume- Issue: 9-11,Page(s):266-271 July2007 [2]. A.Vazquez,E. Antelo, “Conditional speculative decimal addition, “Nancy,France,2006, pp. 47-57. [3]. I.S. Hwang, ”High Speed Binary and Decimal Arithmetic Unit”, United States Patent 2007. [4]. Osama Al-Khaleel,Mohammad Al-Khaleel, Zakariah Al- Qudah “Fast Binary/Decimal Adder/Subtracter with a novel correction free BCD Addition” in IEEE Cinferece on Computer arithmetic, 2011. [5].M.A.Erleand M.J.Shulte “Decimal Multiplication via Carry- Save Addition” (June 2003) IEEE lnt’l Conference on Application Specific system Architectures and Processors, pp .348-358.