Design and Analysis ofFault-Tolerant Digital Systems: B. W. JOHNSON (Addison Wesley, 1989,577 pp., £41.35) The book provides an introduction to the important aspects of designing fault-tolerant systems, and an evaluation of how well the reliability goals have been achieved. The book is mainly oriented towards a final year undergraduate course on fault-tolerant computing, primarily with an implementation bias. In chapters 1 and 2, definitions and basic terminology are covered, which sets the stage for the remaining chapters, and provides the background and motivation for the remainder of the book. Chapter 3 provides a thorough analysis of fault-tolerance techniques and concepts. This chapter in particular is remarkably well written, covering the issues of hardware and information redundancy, which form the mainstay offault-tolerant computing. Subsequent chapters on the use and evaluation of the various approaches illustrate the principles as they have been put into practice. At the end of chapter 5, small projects that allow the reader to apply the material presented in the preceding chapters are included. The resurgence of interest in fault-tolerance with the emergence of VLSI is the theme of chapter 6, focussing on designing fault-tolerant systems in a VLSI environment. The problems and opportunities presented by VLSI are discussed and the use of redundancy techniques in order to enhance manufacturing yield and to provide in-service reliability are reviewed. The final chapter covers testing, design for testability and testability analysis, which must be considered during each phase of the design process to guarantee that resulting designs can be thoroughly tested. Each chapter is followed by a summary of the key issues and concepts presented therein, and a separate list of references, which makes it easily readable. In addition, there is a reading list with more comprehensive and specialised references devoted to each chapter. Overall, the book is well written, and contains a great deal of information in 577 pages. The book has a definite implementation bias, and draws considerably on the author's experience in industry, particularly reflected in the projects accompanying chapter 5. The book should be a useful addition to a library, and a suitable text to accompany a lecture course on fault-tolerant computing. R. RAMASWAMI, Department ofComputation, UMIST

Book Review: Design and Analysis of Fault-Tolerant Digital SystemsDesign and Analysis of Fault-Tolerant Digital Systems: JohnsonB. W. (Addison Wesley, 1989, 577 pp., £41.35)

Wallace high-speed multipliers use full adders and half adders in their reduction phase. Half adders do not reduce the number of partial product bits. Therefore, minimizing the number of half adders used in a multiplier reduction will reduce the complexity. A modification to the Wallace reduction is presented that ensures that the delay is the same as for the conventional Wallace reduction. The modified reduction method greatly reduces the number of half adders; producing implementations with 80 percent fewer half adders than standard Wallace multipliers, with a very slight increase in the number of full adders.

A Reduced Complexity Wallace Multiplier Reduction

With growing interest in the use of SRAM-based FPGAs in space and other radiation environments, there is a greater need for efficient and effective fault-tolerant design techniques specific to FPGAs. Triple-modular redundancy (TMR) is a common fault mitigation technique for FPGAs and has been successfully demonstrated by several organizations. This technique, however, requires significant hardware resources. This paper evaluates three additional mitigation techniques and compares them to TMR. These include quadded logic, state machine encoding, and temporal redundancy, all well-known techniques in custom circuit technologies. Each of these techniques are compared to TMR in both area cost and fault tolerance. The results from this paper suggest that none of these techniques provides greater reliability and often require more resources than TMR.

A Comparison of TMR With Alternative Fault-Tolerant Design Techniques for FPGAs

For many years, most computer architects have pursued one primary goal: performance. Architects have translated the ever-increasing abundance of ever-faster transistors provided by Moore's law into remarkable increases in performance. Recently, however, the bounty provided by Moore's law has been accompanied by several challenges that have arisen as devices have become smaller, including a decrease in dependability due to physical faults. In this book, we focus on the dependability challenge and the fault tolerance solutions that architects are developing to overcome it. The two main purposes of this book are to explore the key ideas in fault-tolerant computer architecture and to present the current state-of-the-art - over approximately the past 10 years - in academia and industry. Table of Contents: Introduction / Error Detection / Error Recovery / Diagnosis / Self-Repair / The Future

Fault Tolerant Computer Architecture

Carry-select adders are one of the faster types of adders. This paper proposes a scheme that encodes the sum bits using two-rail codes; the encoded sum bits are then checked by self-checking checkers. The multiplexers used in the adder are also totally self-checking. The scheme is illustrated with the implementation of a 2-bit carry select adder that can detect all single stuck-at faults on-line; the detection of double faults is not guaranteed. Adders of arbitrary size can be constructed by cascading the appropriate number of such 2-bit adders. A range of adders from 4 to 128 bits is designed using this approach employing a 0.5-mum CMOS technology. The transistor overhead in implementing these self-checking adders varies from 19.51% to 20.94%, and the area overhead varies from 16.07% to 20.67% compared to adders without built-in self-checking capability.

Self-Checking Carry-Select Adder Design Based on Two-Rail Encoding

The two well-known fast multipliers are those presented by Wallace and Dadda. Both consist of three stages. In the first stage, the partial product matrix is formed. In the second stage, this partial product matrix is reduced to a height of two. In the final stage, these two rows are combined using a carry propagating adder. In the Wallace method, the partial products are reduced as soon as possible. In contrast, Dadda's method does the minimum reduction necessary at each level to perform the reduction in the same number of levels as required by a Wallace multiplier. It is generally assumed that, for a given size, the Wallace multiplier and the Dadda multiplier exhibit similar delay. This is because each uses the same number of pseudo adder levels to perform the partial product reduction. Although the Wallace multiplier uses a slightly smaller carry propagating adder, usually this provides no significant speed advantage. A closer examination of the delays within these two multipliers reveals this assumption to be incorrect. This paper presents a detailed analysis for several sizes of Wallace and Dadda multipliers. These results indicate that despite the presence of the larger carry propagating adder, Dadda's design yields a slightly faster multiplier.

A comparison of Dadda and Wallace multiplier delays

This paper presents a concurrent error correcting adder design employing fault masking through a combination of time and hardware redundancy. This new method, Quadruple Time Redundancy, is compared with a non-redundant adder, a Tripple Modular Redundancy adder, and a Time Shared Triple Modular Redundancy adder with respect to the hardware complexity and the delay for adders of various sizes. In comparison with Time Shared Triple Modular Redundancy to which it is most closely related, Quadruple Time Redundancy results in a 40% - 55% reduction in hardware complexity while incurring a reasonable delay increase.

Quadruple Time Redundancy Adders

Fault tolerance requires the inclusion of redundant information. In this paper an on-line error detecting adder is presented in which the redundant information serves a dual purpose. It provides fault tolerance during the arithmetic operations while also providing a method by which addition is constrained to become a constant delay operation regardless of the word size of the operands.

Whitney J. Townsend

Papers

A comparison of Dadda and Wallace multiplier delays

Quadruple Time Redundancy Adders

On-line error detecting constant delay adder