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About: Two's Complement and Fractional Arithmetic for 16-bit Processors

Module by: Douglas L. Jones, Swaroop Appadwedula, Matthew Berry, Mark Haun, Dima Moussa, Daniel Sachs, Jason Laska

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Name: Two's Complement and Fractional Arithmetic for 16-bit Processors
ID: m10808
Language: English (en)
Summary: Two's-complement notation is a mathematically convenient way of representing signed numbers in microprocessors. The most significant bit of a two's complement number represents its sign, and the remaining bits represent its magnitude. Fractional arithmetic allows one to multiply numbers on an integer processor without incurring overflow. Fractional arithmetic requires sign-extension of multipliers and multiplicands, and it requires the product of two numbers to be left-shifted one bit.
Subject: Science and Technology
Keywords: DSP, fractional arithmetic, overflow, two's complement
Document Type: -//CNX//DTD CNXML 0.5 plus MathML//EN
License: Creative Commons Attribution License (CC-BY 1.0)
Authors: Douglas L. Jones (dl-jones@uiuc.edu), Swaroop Appadwedula (appadwed@uiuc.edu), Matthew Berry (mjberry@uiuc.edu), Mark Haun (markhaun@uiuc.edu), Dima Moussa (dmoussa@uiuc.edu), Daniel Sachs (sachs@uiuc.edu), Jason Laska (laska@rice.edu)
Copyright Holders: Douglas L. Jones (dl-jones@uiuc.edu), Swaroop Appadwedula (appadwed@uiuc.edu), Matthew Berry (mjberry@uiuc.edu), Mark Haun (markhaun@uiuc.edu), Dima Moussa (dmoussa@uiuc.edu), Daniel Sachs (sachs@uiuc.edu), Jason Laska (laska@rice.edu)
Maintainers: Mark Butala (butala@uiuc.edu), Matthew Berry (mjberry@uiuc.edu), Robert Morrison (rlmorris@uiuc.edu), Jason Laska (laska@rice.edu)
Version: 2.9 (history)
Created: Aug 14, 2002 12:00 am GMT-5
Revised: Jan 30, 2005 12:51 pm US/Central

Version History

Version: 2.9 Jan 30, 2005 12:51 pm US/Central by Jason Laska
Changes: 
Content fixes
Version: 2.8 Jan 27, 2005 9:25 am US/Central by Robert Morrison
Changes: 
Added Jason Laska
Version: 2.7 Feb 25, 2004 12:18 pm US/Central by Adan Galvan
Changes: 
added maintainer
Version: 2.6 Aug 1, 2003 4:01 pm GMT-5 by Elizabeth Gregory
Changes: 
Updated to 0.5 and added MathML
Version: 2.5 Apr 29, 2003 12:00 am GMT-5 by Matthew Berry
Changes: 
typo in example: was 16348, is 16384
Version: 2.4 Sep 12, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
Fixed mistake in example.  Thanks Mark H.
Version: 2.3 Sep 5, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
added a maintainer
Version: 2.2 Aug 26, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
edited for style and content
edited metadata
Version: 2.1 Aug 19, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
created new module (split content from old m10022)
edited old text for content and style
edited metadata
Version: 2.0 Aug 14, 2002 12:00 am GMT-5 by (Unknown)
Changes: 
Added initial template for new module m10808

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How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 1.0) of this work:

American Chemical Society (ACS) Style Guide:

Jones, D.; Appadwedula, S.; Berry, M.; Haun, M.; Moussa, D.; Sachs, D.; Laska, J. Two's Complement and Fractional Arithmetic for 16-bit Processors, Connexions Web site. http://cnx.org/content/m10808/2.9/, Jan 30, 2005.

American Medical Assocation (AMA) Manual of Style:

Jones D, Appadwedula S, Berry M, et al. Two's Complement and Fractional Arithmetic for 16-bit Processors [Connexions Web site]. January 30, 2005. Available at: http://cnx.org/content/m10808/2.9/.

American Psychological Assocation (APA) Publication Manual:

Jones, D., Appadwedula, S., Berry, M., Haun, M., Moussa, D., Sachs, D., & Laska, J. (2005, January 30). Two's Complement and Fractional Arithmetic for 16-bit Processors. Retrieved from the Connexions Web site: http://cnx.org/content/m10808/2.9/

Chicago Manual of Style (Bibliography):

Jones, Douglas, Swaroop Appadwedula, Matthew Berry, Mark Haun, Dima Moussa, Daniel Sachs, and Jason Laska. "Two's Complement and Fractional Arithmetic for 16-bit Processors." Connexions. January 30, 2005. http://cnx.org/content/m10808/2.9/.

Chicago Manual of Style (Note):

Douglas Jones and others, "Two's Complement and Fractional Arithmetic for 16-bit Processors," Connexions, January 30, 2005, http://cnx.org/content/m10808/2.9/.

Chicago Manual of Style (Reference, in Author-Date style):

Jones, D., Appadwedula, S., Berry, M., Haun, M., Moussa, D., Sachs, D., & Laska, J. 2005. Two's Complement and Fractional Arithmetic for 16-bit Processors. Connexions, January 30, 2005. http://cnx.org/content/m10808/2.9/.

Modern Languages Association (MLA) Style Manual:

Jones, Douglas, Swaroop Appadwedula, Matthew Berry, Mark Haun, Dima Moussa, Daniel Sachs, and Jason Laska. Two's Complement and Fractional Arithmetic for 16-bit Processors. Connexions. 30 Jan. 2005 <http://cnx.org/content/m10808/2.9/>.