A Review - Quaternary Signed Digit Number System by Reversible Logic Gate

A limitation is applied over the speed of latest computers while performing the arithmetic functions such as subtraction, addition & multiplication have to deal with delay in propagation. The arithmetic operations that are free of carry are attained by implementation of high level radix number system such as QSD. We suggest high speed adders constituted over QSD number system. In QSD, every digit is presented by a number in between -3 to 3. The operations on greater numbers like 64, 128 & addition that is carry free is implemented with a persistent delay & low complicacy. In this document, a reversible logic gate is implemented that is constituted over QSD. The performance of QSD adder can be improvised by invading adder based over logic gate that absorbs low power & delay

A high-performance inner-product processor for real and complex numbers.

A novel, high-performance fixed-point inner-product processor based on a redundant binary number system is investigated in this dissertation. This scheme decreases the number of partial products to 50%, while achieving better speed and area performance, as well as providing pipeline extension opportunities. When modified Booth coding is used, partial products are reduced by almost 75%, thereby significantly reducing the multiplier addition depth. The design is applicable for digital signal and image processing applications that require real and/or complex numbers inner-product arithmetic, such as digital filters, correlation and convolution. This design is well suited for VLSI implementation and can also be embedded as an inner-product core inside a general purpose or DSP FPGA-based processor. Dynamic control of the computing structure permits different computations, such as a variety of inner-product real and complex number computations, parallel multiplication for real and complex numbers, and real and complex number division. The same structure can also be controlled to accept redundant binary number inputs for multiplication and inner-product computations. An improved 2's-complement to redundant binary converter is also presented

RADIX-10 PARALLEL DECIMAL MULTIPLIER

This paper introduces novel architecture for Radix-10 decimal multiplier. The new generation of highperformance decimal floating-point units (DFUs) is demanding efficient implementations of parallel decimal multiplier. The parallel generation of partial products is performed using signed-digit radix-10 recoding of the multiplier and a simplified set of multiplicand multiples. The reduction of partial products is implemented in a tree structure based on a new algorithm decimal multioperand carry-save addition that uses a unconventional decimal-coded number systems. We further detail these techniques and it significantly improves the area and latency of the previous design, which include: optimized digit recoders, decimal carry-save adders (CSA’s) combining different decimal-coded operands, and carry free adders implemented by special designed bit counters

The implementation and applications of multiple-valued logic

Multiple-Valued Logic (MVL) takes two major forms. Multiple-valued circuits can implement the logic directly by using multiple-valued signals, or the logic can be implemented indirectly with binary circuits, by using more than one binary signal to represent a single multiple-valued signal. Techniques such as carry-save addition can be viewed as indirectly implemented MVL. Both direct and indirect techniques have been shown in the past to provide advantages over conventional arithmetic and logic techniques in algorithms required widely in computing for applications such as image and signal processing. It is possible to implement basic MVL building blocks at the transistor level. However, these circuits are difficult to design due to their non binary nature. In the design stage they are more like analogue circuits than binary circuits. Current integrated circuit technologies are biased towards binary circuitry. However, in spite of this, there is potential for power and area savings from MVL circuits, especially in technologies such as BiCMOS. This thesis shows that the use of voltage mode MVL will, in general not provide bandwidth increases on circuit buses because the buses become slower as the number of signal levels increases. Current mode MVL circuits however do have potential to reduce power and area requirements of arithmetic circuitry. The design of transistor level circuits is investigated in terms of a modern production technology. A novel methodology for the design of current mode MVL circuits is developed. The methodology is based upon the novel concept of the use of non-linear current encoding of signals, providing the opportunity for the efficient design of many previously unimplemented circuits in current mode MVL. This methodology is used to design a useful set of basic MVL building blocks, and fabrication results are reported. The creation of libraries of MVL circuits is also discussed. The CORDIC algorithm for two dimensional vector rotation is examined in detail as an example for indirect MVL implementation. The algorithm is extended to a set of three dimensional vector rotators using conventional arithmetic, redundant radix four arithmetic, and Taylor's series expansions. These algorithms can be used for two dimensional vector rotations in which no scale factor corrections are needed. The new algorithms are compared in terms of basic VLSI criteria against previously reported algorithms. A pipelined version of the redundant arithmetic algorithm is floorplanned and partially laid out to give indications of wiring overheads, and layout densities. An indirectly implemented MVL algorithm such as the CORDIC algorithm described in this thesis would clearly benefit from direct implementation in MVL

Decimal Floating-point Fused Multiply Add with Redundant Number Systems

The IEEE standard of decimal floating-point arithmetic was officially released in 2008. The new decimal floating-point (DFP) format and arithmetic can be applied to remedy the conversion error caused by representing decimal floating-point numbers in binary floating-point format and to improve the computing performance of the decimal processing in commercial and financial applications. Nowadays, many architectures and algorithms of individual arithmetic functions for decimal floating-point numbers are proposed and investigated (e.g., addition, multiplication, division, and square root). However, because of the less efficiency of representing decimal number in binary devices, the area consumption and performance of the DFP arithmetic units are not comparable with the binary counterparts. IBM proposed a binary fused multiply-add (FMA) function in the POWER series of processors in order to improve the performance of floating-point computations and to reduce the complexity of hardware design in reduced instruction set computing (RISC) systems. Such an instruction also has been approved to be suitable for efficiently implementing not only stand-alone addition and multiplication, but also division, square root, and other transcendental functions. Additionally, unconventional number systems including digit sets and encodings have displayed advantages on performance and area efficiency in many applications of computer arithmetic. In this research, by analyzing the typical binary floating-point FMA designs and the design strategy of unconventional number systems, ``a high performance decimal floating-point fused multiply-add (DFMA) with redundant internal encodings" was proposed. First, the fixed-point components inside the DFMA (i.e., addition and multiplication) were studied and investigated as the basis of the FMA architecture. The specific number systems were also applied to improve the basic decimal fixed-point arithmetic. The superiority of redundant number systems in stand-alone decimal fixed-point addition and multiplication has been proved by the synthesis results. Afterwards, a new DFMA architecture which exploits the specific redundant internal operands was proposed. Overall, the specific number system improved, not only the efficiency of the fixed-point addition and multiplication inside the FMA, but also the architecture and algorithms to build up the FMA itself. The functional division, square root, reciprocal, reciprocal square root, and many other functions, which exploit the Newton's or other similar methods, can benefit from the proposed DFMA architecture. With few necessary on-chip memory devices (e.g., Look-up tables) or even only software routines, these functions can be implemented on the basis of the hardwired FMA function. Therefore, the proposed DFMA can be implemented on chip solely as a key component to reduce the hardware cost. Additionally, our research on the decimal arithmetic with unconventional number systems expands the way of performing other high-performance decimal arithmetic (e.g., stand-alone division and square root) upon the basic binary devices (i.e., AND gate, OR gate, and binary full adder). The proposed techniques are also expected to be helpful to other non-binary based applications

Programmable rate modem utilizing digital signal processing techniques

The engineering development study to follow was written to address the need for a Programmable Rate Digital Satellite Modem capable of supporting both burst and continuous transmission modes with either binary phase shift keying (BPSK) or quadrature phase shift keying (QPSK) modulation. The preferred implementation technique is an all digital one which utilizes as much digital signal processing (DSP) as possible. Here design tradeoffs in each portion of the modulator and demodulator subsystem are outlined, and viable circuit approaches which are easily repeatable, have low implementation losses and have low production costs are identified. The research involved for this study was divided into nine technical papers, each addressing a significant region of concern in a variable rate modem design. Trivial portions and basic support logic designs surrounding the nine major modem blocks were omitted. In brief, the nine topic areas were: (1) Transmit Data Filtering; (2) Transmit Clock Generation; (3) Carrier Synthesizer; (4) Receive AGC; (5) Receive Data Filtering; (6) RF Oscillator Phase Noise; (7) Receive Carrier Selectivity; (8) Carrier Recovery; and (9) Timing Recovery