Decimal Adder Research Articles

Design and study of silicon microring resonator based all-optical binary-coded decimal adder

Design and study of silicon microring resonator based all-optical binary-coded decimal adder

Designs of BCD Adder Based on Excess-3 Code in Quantum-Dot Cellular Automata

Quantum-dot cellular automata (QCA) is a novel nano-electronic technology. QCA has attracted wide attention due to its extremely small feature sizes at the molecular or even atomic scale and ultra-low power consumption, making it a promising candidate to replace the complementary metal oxide semiconductor (CMOS) technology. Binary-Coded Decimal (BCD) adders are widely used in industrial computing. In this paper, we propose two types of excess-3 code (XS-3) based BCD adders (XS-3DAs). We use ripple-carry adders (RCA) and parallel binary adders (PBA) to construct XS-3DAs in QCA Designer tool, respectively. The PBA-based XS-3DA is constructed with a new correction logic. 4-bit, 8-bit, and 16-bit XS-3DAs are constructed based on the two proposed XS-3DAs, respectively. Comparisons show that, with the increase of design scaling, the delay and area-delay product (ADP) of the PBA-based XS-3DAs can be significantly reduced in comparison with that of the RCA-based XS-3DAs. Compared with the 16-digit RCA-based XS-3DA, the cell count, area, delay and ADP of the proposed 16-digit PBA-based XS-3DA are reduced by 37.88%, 25.99%, 37.68% and 53.88%, respectively.

Design of BCD Adder Using QCA Technology

Abstract: Quantum-dot Cellular Automata (QCA) technology is a promising alternative to traditional complementary metaloxide-semiconductor (CMOS) technology for implementing digital circuits due to its potential for high speed, low power consumption, and small size. In this paper, we present a design for a Binary Coded Decimal (BCD) adder using QCA technology. The BCD adder is a crucial building block for arithmetic operations in decimal representation. The proposed design uses QCA cells to perform the addition operation of two BCD digits, which are encoded as a 4-bit binary number. The design includes a full-adder circuit, a BCD-to-binary converter, and a carry-lookahead adder. Simulation results using QCA Designer software demonstrate the functionality and feasibility of the proposed BCD adder design. The proposed design provides a promising alternative to traditional CMOS-based BCD adders and can contribute to the development of QCA-based digital circuits

Efficient architecture for arithmetic designs using perpendicular NanoMagnetic Logic

As the process of scaling down continues at a rapid pace, there is a growing need for an alternative semiconductor device to replace CMOS. One of the alternatives that attracted a lot of attention is called nanomagnetic logic (NML). This is because NML delivers a high device density in addition to a non-volatility of stored information, beyond-CMOS technologies, and device work at room temperature. It is necessary to lower the circuit density and increase the speed of circuits like adders. Using emerging NML logic, we created a full-adder, and ripple carry adder (RCA) with a minimum area. As a result, the invented multilayer-based decimal design makes use of RCA, and full-adder, for innovative 3D topology. We used an NML framework built with perpendicular nanomagnetic (pNML) layers to simulate the characteristics of these devices. With the adder designs that have been offered the latency values are relatively low while performing exhaustive testing. Using pNML technology, a decimal adder has been constructed for the first time in the literature. In addition, simulations are carried out with the help of the Modelsim simulator. During the process of nanomagnetic designing consideration is given to both of these aspects as latency and area. To create an NML circuit, the tool MagCAD is employed. Results are better using the pNML environment-based full adder, RCA and decimal adder.

Design of efficient binary-coded decimal adder in QCA technology with a regular clocking scheme

Quantum-dot cellular automata (QCA) is a promising nanotechnology that offers an alternative to complementary metal-oxide-semiconductor (CMOS) technology. Nanoscale size, ultra-low power dissipation, and Terahertz range operating frequency make QCA more attractive to circuit designers. Recently, numerous designs of QCA have been proposed but aren't practically implementable due to random clocks in the design. In QCA designs, there is a need for proper clocking scheme to favour placement and routing and to facilitate QCA nano-computing synthesis. In this paper, a novel design of Binary-Coded Decimal (BCD) adder, based on QCA technology, with a realistic clocking scheme is presented. System simulations of the proposed designs are performed using QCA designer software Ver. 2.0.3 while power dissipation is investigated using the QCA Pro tool. Besides, in terms of power dissipation, the suggested QCA BCD adder dissipates 2.788 × 10−5 mW, whereas CMOS- based design consume 1.34 mW of power.

AMPS: An Automated Mesochronous Pipeline Scheduler and Design Space Explorer for High Performance Digital Circuits

In the Mesochronous Pipeline (MP), the clock period is the maximal of differences between the maximum/minimum delays of all stages. This value is less than the maximum delay between the memory elements, so MP is operating faster than the conventional pipeline (CP). To take full advantages of MP, in this paper, Automated Mesochronous Pipeline Scheduler (AMPS) for high performance digital circuits, is proposed which provides all allowed partitioning options generated by register allocation procedures obtained with varying maximum delay differences of stages. This allows a designer to select from design space produced by AMPS based on the desired specification. Unlike the traditional MP, AMPS utilizes automated scripts to extract the timing characteristics of the synchronizers and gates. This enables a designer to explore trade-offs between latency, power, and frequency. To evaluate our toolset, an 8-bit Carry Increment Adder (CIA), a 4-bit Binary-Coded Decimal (BCD) adder, a 4-bit ALU, and a set of circuits from ISCAS85 and ISCAS89 benchmarks are considered. All circuit level simulations are performed in the 65nm CMOS standard technology node. AMPS improves the frequency for its best solutions about 127.94% (on average) in comparison to the conventional pipeline scheme.

Impact of Radix-10 Redundant Digit Set [−6, 9] on Basic Decimal Arithmetic Operations

Redundant-digit decimal computer arithmetic, with the principal property of carry-free addition, has been the subject of several studies, as the relevant literature contains a wide variety of decimal digit sets and their binary representations. For example, symmetric decimal signed digit sets [-α, α], for α ∈ {5,6,7,8,9 }, and the asymmetric ones, such as [-8,9], [ -9,7], and [ 0,15 ], have been the basis of variant hardware architectures for decimal arithmetic operations. However, digit sets with the minimal 4-bit representations show better figures of merit. In this work, we present a new decimal digit set [-6,9], called diminished-6 overloaded decimal digit set (DODDS). Its special 4-bit representation contains two posibits (weighted 2³ and 2⁰) and two negabits (weighted 2² and 2¹). Design and implementation of the corresponding carry-free decimal adders and subtractors are thoroughly discussed. Furthermore, to cover the requirements of all possible DODDS applications in decimal multipliers, dividers, and square rooters, we provide adder/subtractor designs for a variety of input combinations of DODDS and binary coded decimal (BCD) operands, all with DODDS output (e.g., DODDS + BCD = DODDS, which is useful in BCD partial product reduction). Analytical and synthesis-based evaluations and comparisons with similar previous works show the notable merits of DODDS over the other redundant decimal digit sets.

Implementation of Quantum-Dot Cellular Automata Based Efficient N-Bit BCD Adders Using Verilog

Quantum Dot Handheld Automatics is one of the best technologies in recent days for introducing a high speed and ultra-low powered digital circuit. Few binary and decimal arithmetic circuits were designed using an efficacious QCA-based algorithm. However, there is a substantial enhancement required yet if there is inbuilt availability of logic gates inside the QCA. Therefore, this article introduced innovative binary coded decimal (BCD) adders using QCA methodology. Simulation analysis discloses that proposed BCD adders obtained higher computational speed with lower delays and lesser area than conventional CMOS approaches.

On The Implementation of Densely Packed Decimal Number System Based Adder: Prospects and Challenges

Decimal digit number computation, through bit compression methodology, offers space and time saving, which can be incurred by the Chen-Ho and Densely Packed Decimal (DPD) coding techniques. Such coding techniques have a property of bit compression, like, three decimal digits can be represented by 10 bits instead of 12 bits in binary coded decimal (BCD) format. The compression has been obtained through the elimination of the redundant 0’s from BCD representation. This manuscript reports the pros and cons of the techniques mentioned above. The logic level functionalities have been examined through MATLAB, whereas circuit simulation has been erified through Cadence Spectre. Performance parameters (such as delay, power consumption) have been evaluated through CMOS gpdk45 nm technology. Furthermore, the best design has been chosen from them, and the decimal adder design technique has been incorporated in this paper.

A Parallel Decimal Multiplier Based on a novel 4:2 Fully Redundant Decimal Adder

Due to requirements for computational accuracy in the fields of business computing, the decimal arithmetic computing system has gradually become a research hotspot. A parallel decimal multiplication consists of three stages: partial product generation (PPG), partial product reduction (PPR) and the final product generation (FPG). In the PPR stage, a novel 4:2 fully redundant decimal adder based overloaded decimal digit set (ODDS) is proposed in this paper. The 4:2 ODDS adder is formed by the binary 4:2 compressors, a decimal compressor and a converter. Moreover, the signed-digit radix-10 code, the redundant excess-3 code and the ODDS code are used in the PPG stage. In the FPG stage, an ODDS–BCD conversion is adopted to quickly generate BCD-8421 product. The analysis and comparison by using the 45nm technology show that the proposed decimal multiplier based on the 4:2 ODDS adder has less area and better synthesis performance.

BCD Adder Designs Based on Three-Input XOR and Majority Gates

Lots of emerging techniques can natively realize majority-of-three (MAJ) gates. Although enhanced gates such as exclusive-OR (XOR) gates can be implemented by several MAJ gates, there exists much efficient XOR design which directly derived by the physical attributes of emerging techniques. In this brief, we proposed multi-digit binary coded decimal (BCD) adder designs represented based on three-input exclusive-OR (XOR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) and MAJ gates. BCD adder is widely used in financial, commercial, and industrial computing. We implemented the designs using quantum-dot cellular automata (QCA) technology. The proposed logic representations are validated using different types of binary adders as well as QCA design strategies. The introduction of XOR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> gates is conducive to achieve compact logic representations, which positively affect both the area and delay of QCA layouts. Compared with the existing best designs, the proposed 1-digit BCD adder has 50% less area and 10% less delay, and the 8-digit BCD adder has a 3.42× improvement of area-delay product.

A Novel n-Decimal Reversible Radix Binary-Coded Decimal Multiplier Using Radix Encoding Scheme

Reversible logic has been emerging as a replacement for conventional digital computers and has been found to be a promising technology for the future that can improve the quality of circuits in terms of power, speed, heat dissipation, life span, and input traceability. The new generation of quantum processors demands the efficient implementation of decimal data path elements in many commercial, financial, and Internet-based applications. Reversible binary-coded decimal multipliers are among the important circuits in quantum computers. In this approach, we propose a low-power reversible radix binary-coded decimal multiplier. The proposed methodology uses a novel 4221 reversible recorder gate to select precomputed constant multiples and binary to excess-six conversion reversible decimal adder for partial product compression. The proposed multiplier is designed with 180-nm application-specific integrated circuit technology using the Cadence EDA tool and is compared with state-of-the-art BCD algorithms designed using reversible gates. Experimental evaluations revealed that the proposed design demonstrates power and power-delay product reductions of 28% and 37%, respectively, compared to those of the best BCD algorithms implemented in reversible logic.

New approach to Design of Reversible BCD Adder

Over the last few decades, research in reversible logic has increasingly become very popular and it is gaining greater momentum in the present word. Reversible logic has started finding concert applications in quantum computing, optical computing, nano-technology based system, low-power CMOS design, VLSI design. The principal objective of this work is to argue for quantum implementation of various reversible logic gates by using C-NOT, Controlled-V and Controlled-V+ gates. The present work presents Binary coded decimal adder (BCD) in terms of number of gates, garbage outputs, quantum cost, delay and hardware complexity compared to existing design.

Heterogeneous Adder Based FIR Filter Design And Simulation

The finite impulse response (FIR) is one of the important filters in digital signal processing (DSP) as it responds for a finite duration and settles to zero on the finite time. Digital FIR filters are programmable in nature and its behavior can be understood with the help of the program and can be easily programmed for the memory of a processor. The digital filters can be replaced without change of the hardware or the external circuitry. The 7 tap FIR filter needs 16 numbers of multipliers and 9 adders which are used in parallel form. The paper focused on the chip design and implementation of the FIR filter with a decimal adder and heterogeneous adder is done using VHDL programming in Xilinx 14.2 ISE software and the same is synthesized on SPARTAN - 3E FPGA to verify the results. Moreover, the functional simulation is done in Modelsim 10.0 software. Hardware utilization parameters, combinational path delay, memory utilization parameters are directly extracted from the Xilinx software for FIR filter architecture based on decimal adder and heterogeneous adders. The comparative analysis of the FIR filter is done with heterogeneous adder architecture lead an area and delay efficient design for DSP applications

Design and Implementation of Reduced Power Energy Efficient Binary Coded Decimal Adder

&lt;p&gt;This paper presents a novel architecture for low power energy binary represented decimal addition. The proposed BCD adder uses Binary to Excess Six Converter (BESC) block for constant correction to adjusts binary outputs exceeding 9 to correct decimal values and exploits the inherent advantage of reduced delay and switching, due to elimination of long carry propagation in second stage addition as in conventional design and switching OFF of the BESC block for decimal outputs less than 9. The proposed BESC-BCD adder has been designed using VHDL code and synthesized using Altera Quartus II. Experimental results demonstrates that the proposed decimal adder can lead to significant power savings and delay reduction compared to existing BCD adders which is realised in better power-delay product(PDP) performance. For example the PDP saving of the proposed BESC-BCD adder for a 1 digit and 2 digit addition implementations are 11.6% and 16.05% respectively, compared to the best of the designs used for comparison.&lt;/p&gt;

New Majority Gate-Based Parallel BCD Adder Designs for Quantum-Dot Cellular Automata

In this brief, we first theoretically re-defined output decimal carry in terms of majority gates and proposed a carry lookahead structure for calculating all the intermediate output carries. We have used this method for designing the multi-digit decimal adders. Theoretically, our best ${n}$ -digit decimal adder design reduces the delay and area-delay product by 50% compared with previous designs. We have implemented our designs using QCADesigner tool. The proposed QCADesigner based 8-digit PBA-BCD adder achieves over 38% less delay compared with the best existing designs.

A Power-Efficient Single Layer Full Adder Design in Field-Coupled QCA Nanocomputing

As an emerging technology device, Quantum-dot cellular automata (QCA) may be a suitable substitute for traditional semiconductor transistor technology. Arithmetic logic unit in field-coupled QCA has been also studied extensively in recent year. In this paper, the new low-power Exclusive-OR gate is presented, which is mainly based on QCA cellular leveled format. This Exclusive-OR gate can be used to design various useful QCA circuits. By using this gate, we design and implement a novel full adder circuit with low dissipation. The circuit is designed using only 45 normal cells in a single layer without crossover. Compared with previous designs, both decimal adders achieve better performance in terms of latency and overall cost. The operation of the proposed circuit has been verified by QCADesigner version 2.0.3 and energy dissipation investigated by QCAPro tool. We also compared with previous designs in terms of power dissipation, cell-counts, area, latency and cost. The proposed full adder has the smallest area with less number of cells. And the total energy dissipation of our proposed full adder are only 0.05112 eV, 0.07454 eV and 0.10181 eV when tunneling energy levels are 0.5 Ek, 1 Ek and 1.5 Ek, respectively. The proposed single full adder also has the lowest total energy dissipation with a reduction of 20.94, 11.25 and 4.82% in 0.5 Ek, 1 Ek and 1.5 Ek tunneling energy levels, respectively when compared with the previous most power-efficient design.

Improving the area of fast parallel decimal multipliers

Financial and commercial applications depend on decimal arithmetic because they must produce results that match exactly those obtained by human calculations. Decimal multiplication is a frequently used operation in these applications and also in the design of decimal floating-point units. In this paper we propose a new architecture for parallel decimal multiplication that improves the area of previous decimal multipliers while keeping the best performances. A decimal adder [1] based on a mixed BCD/excess-6 representation of the operands is utilized. A new partial product generation unit is proposed based on a 5221 recoding of the multiplier digits. With the proposed multiplier, we are able to improve on state-of-the-art parallel decimal multipliers targeting LUT-6 FPGAs. Compared to previous decimal multipliers, implementation results for 2, 4, 8, 16, 32 and 34-digits show that the proposed multiplier achieves over 20% better area without performance degradation.

Decimal multiplication using compressor based-BCD to binary converter

The objective of this work is to implement a scalable decimal to binary converter from 8 to 64 bits (i.e 2-digit to 16-digit) using parallel architecture. The proposed converters, along with binary coded decimal (BCD) adder and binary to BCD converters, are used in parallel implementation of Urdhva Triyakbhyam (UT)-based 32-bit BCD multiplier. To increase the performance, compressor circuits were used in converters and multiplier. The designed hardware circuits were verified by behavioural and post layout simulations. The implementation was carried out using Virtex-6 Field Programmable Gate Array (FPGA) and Application Specific Integrated Circuit (ASIC) with 90-nm technology library platforms. The results on FPGA shows that compressor based converters and multipliers produced less amount of propagation delay with a slight increase of hardware resources. In case of ASIC implementation, a compressor based converter delay is equivalent to conventional converter with a slight increase of gate count. However, the reduction of delay is evident in case of compressor based multiplier.

High Performance Parallel Decimal Multipliers Using Hybrid BCD Codes

A parallel decimal multiplier with improved performance is proposed in this paper by exploiting the properties of three different binary coded decimal (BCD) codes, namely the redundant BCD excess-3 code (XS-3), the overloaded decimal digit set (ODDS) code and the BCD-4221/5211 code. The signed-digit radix-10 recoding is used to recode the BCD multiplier to the digit set [-5, 5] from [0, 9]. The redundant BCD XS-3 code is adopted to generate the multiplicand multiples in a carry-free manner. The XS-3 coded partial products (PPs) are converted to ODDS PPs to fit binary partial product reduction (PPR). In this paper, a regular decimal PPR tree using ODDS and BCD-4221/5211 codes is proposed; it consists of a binary PPR tree block, a non-fixed size BCD-4221 counter block and a BCD-4221/5211 PPR tree block. The decimal carry-save algorithm based on BCD-4221/5211 is used in the PPR tree to obtain high performance multipliers. Moreover, an improved PPG circuit and an improved parallel prefix/carry-select decimal adder are proposed to further improve the performance of the proposed multipliers. Analysis and comparison using the 45 nm technology show that the proposed decimal multipliers are faster and require less hardware area than previous designs found in the technical literature.