Abstract
The chapter contains fundamental notions referring to the number representations in computation, in fixed point and in floating point. As regards the fixed point, in distinct sections we analyze the binary numbers and decimal numbers representations. We present, together with their advantages and disadvantages, the representations of fixed point binary numbers in sign-magnitude, ones complement and twos complement codes, in particular aiming toward the addition operation. Referring to the floating point representations, the emphasis is on the issues concerning the biased representation of the exponent and the normalized representation of the mantissa. Moreover, the specific elements corresponding to the IEEE 754 floating point binary number representation standard are detailed.
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References
Randal E. Bryant, David O’Hallaron: “Computer Systems. A Programmer’s Perspective” Pearson Education International, Upper Saddle River, 2003.
Miloš D. Ercegovac, Tomas Lang: “Digital Arithmetic” Morgan Kaufmann, San Mateo, 2004.
John P. Hayes: “Computer Architecture and Organization” McGraw-Hill, New York, Third Edition, 1998.
John L. Hennessy, David A. Patterson: “Computer Architecture. A Quantitative Approach” Morgan Kaufmann, San Mateo, Third Edition, 2003; Appendix H: Computer Arithmetic by David Goldberg.
W. Kahan: “Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic” October 1997, http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF.
Ulrich W. Kulisch: “Advanced Arithmetic for the Digital Computer. Design of Arithmetic Units” Springer, Berlin, 2002.
Amos R. Omondi: “Computer Arithmetic Systems. Algorithms, Architecture and Implementations” 1994. C.A.R. Hoare Series Editor.
Behrooz Parhami: “Computer Arithmetic. Algorithms and Hardware Designs” Oxford University Press, London, 2000.
Sridhar Rajagopal, Joseph R. Cavallaro: “Truncated On-line Arithmetic with Applications to Communication Systems” IEEE Trans. Comput., vol. 55, no. 10, 2006, pp. 1240–1252.
Eric M. Schwarz, Martin Schmookler, Son Dao Trong: “FPU Implementations with Denormalised Numbers” IEEE Trans. Comput., vol. 54, no. 7, 2005, pp. 825–836.
William Stallings: “Computer Organization and Architecture. Designing for Performance” Prentice Hall International, Englewood Cliffs, 1999.
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© 2012 Springer-Verlag Berlin Heidelberg
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Vlăduţiu, M. (2012). The Representation of Numbers in Computing Systems. In: Computer Arithmetic. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18315-7_1
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DOI: https://doi.org/10.1007/978-3-642-18315-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18314-0
Online ISBN: 978-3-642-18315-7
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