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An Approach to Teaching Computer Arithmetic

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2565))

Abstract

In this work we present an initiative to support teaching computer representation of numbers (both integer and floating point) as well as arithmetic in undergraduate courses in computer science and engineering. Our approach is based upon a set of carefully designed practical exercises which highlights the main properties and computational issues of the representation. In conjunction to the exercises, an auxiliary computer-based environment constitutes a valuable support for students to learn and understand the concepts involved. For integer representation, we have focused on the standard format, the well known 2’s complement. For floating point representation, we have made use of an intermediate format as an introduction to the IEEE 754 standard. Such an approach could be included in an introductory course related to either computer structure, discrete mathematics or numerical methods.

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References

  1. C.W. Ueberhuber Numerical Computation. Methods, Software, and Analysis, Vols. 1&2. Springer-Verlag, 1997. 269

    Google Scholar 

  2. D.A. Patterson and J. L. Hennessy. Computer Organization and Design. The Hardware/Software Interface Morgan Kaufmann Pub., 1998. 269, 272

    Google Scholar 

  3. D.E. Knuth. The Art of Computer Programming, 3rd ed, volume 2, Seminumerical Algorithms. Addison-Wesley, 1998. 270

    Google Scholar 

  4. W. Kahan. IEEE Standard 754 for Binary Floating-Point Arithmetic. WWW document, 1996. http://www.cs.berkeley.edu/ wkahan/ieee754status/ieee754.ps. 270

  5. Curriculum 2001 Joint IEEE Computer Society/ACM Task Force. “Year 2001 Model Curricula for Computing ((CC-2001),” Final report, December 15, 2001. 270

    Google Scholar 

  6. T. J. Scott. “Mathematics and computer science at odds over real numbers,” ACM SIGCSE Bulletin, 23(1):130–139, 1991. 270, 271

    Article  Google Scholar 

  7. D. Goldberg. “What every computer scientist should know about floating-point arithmetic,” ACM Comp. Surveys, 23:5–48, 1991. 270

    Article  Google Scholar 

  8. C.W. Steidley. “Floating point arithmetic basic exercises in mathematical reasoning for computer science majors,” Computers in Education Journal, 2(4):1–6, 1992. 270

    Google Scholar 

  9. W. Kahan. Ruminations on the design of floating-point arithmetic. WWW document, 2000. (http://www.cs.nyu.edu/cs/faculty/overton/book/docs/). 270

  10. M. L. Overton. Numerical Computing and the IEEE Floating Point Standard. SIAM, 2001. 270, 271, 274

    Google Scholar 

  11. S. Guelich, S. Gundavaram, G. Birznieks. CGI Programming on the World Wide Web. O'Reilly, 2000. 281

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Garzón, E.M., García, I., Fernández, J.J. (2003). An Approach to Teaching Computer Arithmetic. In: Palma, J.M.L.M., Sousa, A.A., Dongarra, J., Hernández, V. (eds) High Performance Computing for Computational Science — VECPAR 2002. VECPAR 2002. Lecture Notes in Computer Science, vol 2565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36569-9_17

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  • DOI: https://doi.org/10.1007/3-540-36569-9_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00852-1

  • Online ISBN: 978-3-540-36569-3

  • eBook Packages: Springer Book Archive

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