Rekha K. James

Decimal multiplication using compact BCD multiplier

Decimal multiplication is an integral part of financial, commercial, and internet-based computations. The basic building block of a decimal multiplier is a single digit multiplier. It accepts two Binary Coded Decimal (BCD) inputs and gives a product in the range [0, 81] represented by two BCD digits. A novel design for single digit decimal multiplication that reduces the critical path delay and area is proposed in this research. Out of the possible 256 combinations for the 8-bit input, only hundred combinations are valid BCD inputs. In the hundred valid combinations only four combinations require 4 times 4 multiplication, 64 combinations need 3 times 3 multiplication, and the remaining 32 combinations use either 3 times 4 or 4 times 3 multiplication. The proposed design makes use of this property. This design leads to more regular VLSI implementation, and does not require special registers for storing easy multiples. This is a fully parallel multiplier utilizing only combinational logic, and is extended to a Hex/Decimal multiplier that gives either a decimal output or a binary output. The accumulation of partial products generated using single digit multipliers is done by an array of multi-operand BCD adders for an (n-digit times n-digit) multiplication.

A New Look at Reversible Logic Implementation of Decimal Adder

Reversibility plays a fundamental role when computations with minimal energy dissipation are considered. In recent years, reversible logic has emerged as one of the most important approaches for power optimization with its application in low power CMOS, quantum computing and nanotechnology. This research proposes a new implementation of Binary Coded Decimal (BCD) adder in reversible logic. The design reduces the number of gates and garbage outputs compared to the existing BCD adder reversible logic implementations. So, this design gives rise to an implementation with a reduced area and delay.

Performance analysis of double digit decimal multiplier on various FPGA logic families

Decimal multiplication is an integral part of financial, commercial, and internet-based computations. This paper presents a novel double digit decimal multiplication (DDDM) technique that performs 2 digit multiplications simultaneously in one clock cycle. This design offers low latency and high throughput. When multiplying two n-digit operands to produce a 2n-digit product, the design has a latency of [(n/2 +1] cycles. The paper presents area and delay comparisons for 7-digit, 16-digit, 34-digit double digit decimal multipliers on different families of Xilinx, Altera, Actel and Quick Logic FPGAs. The multipliers presented can be extended to support decimal floating-point multiplication for IEEE P754 standard.

Performance analysis of FIR digital filter design: RNS versus traditional

This paper presents performance analysis of Residue Number System (RNS) based Finite Impulse Response (FIR) digital filters and traditional FIR filters. This research is motivated by the importance of an efficient filter implementation for digital signal processing. The comparison is done in terms of speed and area requirement for various filter specifications. RNS based FIR filters operate more than three times faster and consumes only about 60% of the area than traditional fitter when number of filter taps is more than 32. The area for RNS filter is increasing at a lesser rate than that for traditional resulting in low-power consumption. RNS is a non-weighted number system without carry propagation between different residue digits. This enables simultaneous parallel processing on all the digits resulting in high speed addition and multiplication in RNS domain. Such compact and high speed real-time digital filters find applications in radar, communications and image processing systems.

Reversible Binary Coded Decimal Adders using Toffoli Gates

Reversibility plays a fundamental role when computations with minimal energy dissipation are considered. This research describes Toffoli Gate (TG) implementations of conventional Binary Coded Decimal (BCD) adders, adders for Quick Addition of Decimals (QAD), and carry select BCD adders suitable for multi-digit addition. For an N-digit fast adder, partial parallel processing is done on all digits in the decimal domain. Such high-speed BCD adders find application in realtime processors and internet-based computing. An analysis of delay normalized to a TG and quantum cost of BCD adders is presented. Implementations using TGs and Fredkin Gates (FRGs) are compared based on quantum cost, number of gates, garbage count and delay, and the results are tabulated.

High performance, low latency double digit decimal multiplier on ASIC and FPGA

Decimal multiplication is an integral part of financial, commercial, and internet-based computations. This paper presents a novel double digit decimal multiplication (DDDM) technique that offers low latency and high throughput. This design performs two digit multiplications simultaneously in one clock cycle. Double digit fixed point decimal multipliers for 7digit, 16 digit and 34 digit are simulated using Leonardo Spectrum from Mentor Graphics Corporation using ASIC Library. The paper also presents area and delay comparisons for these fixed point multipliers on Xilinx, Altera, Actel and Quick logic FPGAs. This multiplier design can be extended to support decimal floating point multiplication for IEEE 754- 2008 standard.

RNS Based Programmable Multi-Mode Decimation Filter for WCDMA and WiMAX

The recent trends envisage multi-standard architectures as a promising solution for the future wireless transceivers to attain higher system capacities and data rates. The computationally intensive decimation filter plays an important role in channel selection for multi-mode systems. An efficient reconfigurable implementation is a key to achieve low power consumption. To this end, this paper presents a dual-mode Residue Number System (RNS) based decimation filter which can be programmed for WCDMA and 802.16e standards. Decimation is done using multistage, multirate finite impulse response (FIR) filters. These FIR filters implemented in RNS domain offers high speed because of its carry free operation on smaller residues in parallel channels. Also, the FIR filters exhibit programmability to a selected standard by reconfiguring the hardware architecture. The total area is increased only by 24% to include WiMAX compared to a single mode WCDMA transceiver. In each mode, the unused parts of the overall architecture is powered down and bypassed to attain power saving. The performance of the proposed decimation filter in terms of critical path delay and area are tabulated.

Fixed Point Decimal Multiplication Using RPS Algorithm

Decimal multiplication is an integral part of financial, commercial, and Internet-based computations. A novel design for single digit decimal multiplication that reduces the critical path delay and area for an iterative multiplier is proposed in this research. The partial products are generated using single digit multipliers, and are accumulated based ona novel RPS algorithm. This design uses n single digit multipliers for an n times n multiplication. The latency for the multiplication of two n-digit Binary Coded Decimal (BCD) operands is (n + 1) cycles and a new multiplication can begin every n cycle. The accumulation of final partial products and the first iteration of partial product generation for next set of inputs are done simultaneously. This iterative decimal multiplier offers low latency and high throughput, and can be extended for decimal floating-point multiplication.

Dual-mode RNS based programmable decimation filter for WCDMA and WLANa

The recent trends envisage multi-standard architectures as a promising solution for the future wireless transceivers. The computationally intensive decimation filter plays an important role in channel selection for multi-mode systems. An efficient reconfigurable implementation is a key to achieve low power consumption. To this end, this paper presents a dual-mode Residue Number System (RNS) based decimation filter which can be programmed for WCDMA and 802.11a standards. Decimation is done using multistage, multirate finite impulse response (FIR) filters. These FIR filters implemented in RNS domain offers high speed because of its carry free operation on smaller residues in parallel channels. Also, the FIR filters exhibit programmability to a selected standard by reconfiguring the hardware architecture. The total area is increased only by 33% to include WLANa compared to a single mode WCDMA transceiver. In each mode, the unused parts of the overall architecture is powered down and bypassed to attain power saving. The performance of the proposed decimation filter in terms of critical path delay and area are tabulated.

Quick Addition of Decimals Using Reversible Conservative Logic

In recent years, reversible logic has emerged as one of the most important approaches for power optimization with its application in low power CMOS, nanotechnology and quantum computing. This research proposes quick addition of decimals (QAD) suitable for multi-digit BCD addition, using reversible conservative logic. The design makes use of reversible fault tolerant Fredkin gates only. The implementation strategy is to reduce the number of levels of delay there by increasing the speed, which is the most important factor for high speed circuits.