by Tsun Tak-on. / Chinese title: / Bibliography: leaves 111-113 / Thesis (M.Phil.)--Chinese University of Hong Kong, 1983

Title also in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaves 159-161.

Minimizing the dynamic power consumption of a circuit is becoming a more and more important issue for digital circuit design in the age of portable electronics. Among all the arithmetic circuits, addition is the most fundamental operation. Therefore, designing low power adder is an important and necessary research area. In this thesis, the dynamic switching power consumption of ripple carry adder, carry look ahead adder, carry skip adder, carry select adder, and prefix adder are discussed. The power factor, the sum of products of probability and fan-out of all internal nodes, is presented. This thesis also studies the power and time trade-off with efficiency index which is the product of power factor and worst case gate counts. The result shows that the carry look ahead adder has the lowest efficiency index in the design of a 64 bit adder. The carry skip adder is the best one in a design of a 16 and 32 bit adder. The ripple carry adder is the best choice for an 8 bit adder. This study also presents a low power prefix adder design which will reduce the power consumption of the prefix adder without lost of performance. / Graduation date: 1998

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 98-102).

In this dissertation, the design and analysis of several fast arithmetic components are presented. Our contributions focus on the fast CORDIC rotation architectures and multipliers. In the CORDIC design, we proposed a fast rotation architecture that can reduce by half the average number of rotations. Furthermore, a new parallel CORDIC rotation algorithm and architecture (called para-CORDIC) is proposed that leads to smaller area and delay compared with the conventional CORDIC algorithm and previous works. In the design of the multiplier generator, a delay-efficient algorithm is used to perform the partial products summation and the final addition during the synthesis of fast parallel multipliers based on standard cell library or other full-custom circuit components. In the field of fixed-width multiplier designs, a lower-error fixed-width carry-free multiplier with low-cost compensation circuits is proposed that has smaller absolute average errors and variances compared with pervious methods.

In many digital signal processing applications, we often need some special function units which can compute complicated arithmetic functions such as reciprocal and logarithm. Conventionally, table-based arithmetic design strategy uses lookup tables to implement these kinds of function units. However, the table size will increase exponentially with respect to the required precision. In this thesis, we propose two methods to reduce the table size: bottom-up non-uniform segmentation and the approach which merges uniform piecewise interpolation and Newton-Raphson method. Experimental results show that we obtain significant table sizes reduction in most cases.

Thesis (M.S.)--Ohio University, March, 1999. / Title from PDF t.p.

No description available.

No description available.

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.