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Digital logic design : a rigorous approach
Even G., Medina M., Cambridge University Press, New York, NY, 2012. 368 pp. Type: Book (978-1-107027-53-4)
Date Reviewed: Jun 20 2013

While this book may appear overly formal, an exposure to this type of teaching is mandatory for any advanced student of digital logic design. As an analogy, probability theory can be taught with excellent results in an informal setting, but exposure to the rigorous measure theory is mandatory for advanced students in the field.

The text is mostly self-contained. Part 1 contains the basic definitions and theorems from the relevant portions of set theory and directed graphs, as well as a concise introduction to binary representation of natural numbers. This part of the book also includes a chapter on propositional logic as applied to Boolean functions, which are at the foundation of digital design the way it is dominantly practiced today.

Part 2 starts with a chapter on the representation of Boolean functions, truth tables, and the Quine-McCluskey method for the shortest representation. The next chapter, chapter 10, introduces the mapping of Boolean variables into the physical world of their realization in a digital device. Chapter 11 lays the foundation of combinational circuits, with the stated goal of proving that every Boolean function can be implemented by a combinational circuit, and further, that every combinational circuit implements a Boolean function.

The next chapter provides a proof that the natural partitioning for computing a multi-bit Boolean function, which leads to a rooted tree, is indeed optimal in terms of cost, and that a balanced tree is optimal in terms of delay. Chapters 13 and 14 introduce the basic building blocks beyond simple gates, including encoders and decoders, multiplexers, and shifters. Chapters 15 and 16 introduce the basic arithmetic circuit, the adder, for both positive and negative numbers. The two’s complement representation of negative numbers is also described in this section.

Part 3 is entirely devoted to synchronous circuits, starting with a thorough discussion of the flip-flop, the basic one-bit memory element for synchronous circuit implementations. The authors prove an interesting theorem about the impossibility of having an arbiter, and introduce the necessity of so-called critical segments. The natural extension from simple flip-flops to registers and memories follows in chapter 18. Building on the background material from the previous two chapters, chapter 19 delves into the intricacies of synchronous circuits. The last chapter of this part deals with some aspects of the analysis and synthesis of finite state machines, using examples of counters and serial adders.

The last part of the book details the instruction set architecture, and the operation of a simple processor, the simplified DLX machine.

I highly recommend this book for academic courses on digital design. Readers looking for a faster and more practical introduction to digital design will most likely skip it.

Reviewer:  Vladimir Botchev Review #: CR141300 (1309-0761)
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Types And Design Styles (B.7.1 )
 
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