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This book explains, in lay terms, the surprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in its style and often funny, it follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. ONES AND ZEROS will be enjoyed by anyone who has a general interest in science and technology.
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ONES AND ZEROS
IEEE Press Understanding Science & Technology Series The IEEE Press Understanding Series treats important topics in science and technology in a simple and easy-to-understand manner. Designed expressly for the nonspecialist engineer, scientist, or technician, as well as the technologically curious-each volume stresses practical information over mathematical theorems and complicated derivations.
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ONES AND ZEROS Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets
John Gregg
IEEE Press Understanding Science & Technology Series Dr. Mohamed E. El-Hawary, Series Editor
+IEEE The Institute of Electrical and Electronics Engineers, lnc.,NewYork
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IEEE Press 445 Hoes Lane, P.O. Box 1331 Piscataway, NJ 08855·1331 IEEE Press Editorial Board Roger F. Hoyt, Editor in Chief J. B. Anderson P. M. Anderson M. Eden M. E. El-Hawary
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Furui A. H. Haddad R. Herrick S. Kartalopoulos D. Kirk
P. Laplante M. Padgett W. D. Reeve G. Zobrist
Kenneth Moore, Director of IEEE Press John Griffin, Senior Acquisitions Editor Linda Matarazzo, Assistant Editor Denise Phillip, Associate Production Editor Cover design: Caryl Silvers, Silvers Design
Technical Reviewers Sherif Embabi, Texas A&M University Starn Kartalopoulos, Lucent Technologies, Bell Labs Innovations Richard S. Muller, University of California, Berkeley Kevin D. Taylor, Purdue University at Kokomo Neal S. Widmer, Purdue University, EET Department
To Susan, without whom this book would have been finished a lot sooner.
B, but which cascades from right to left. That is, information is passed within the comparator from the cell in the least significant bit position to bit positions of successively greater significance until the output of the cell in the most significant bit position is taken as the output of the entire comparator.
6.5 THE ALU We can now apply our knowledge of adders, multiplexers, and multi-bit parallel operations to build a controllable, multiple-function digital circuit called an arithmetic logic unit (ALU). The ALU is the heart of a central processing unit (CPU),
Chapter 6
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More Digital Circuits
which itself is the heart of a computer. In a rather limited sense, it is a computer itself, in that it performs anyone of a variety of functions depending on an externally provided command. Our simple ALU will deal with six-bit numbers. It will yield a six-bit number as output, and it will u