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mws_gen_aae_spe_pptbinaryrepresentation(1)

# mws_gen_aae_spe_pptbinaryrepresentation(1) - Binary...

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1/11/2010 http://numericalmethods.eng.usf.edu 1 Binary Representation Major: All Engineering Majors Authors: Autar Kaw, Matthew Emmons http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates

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Binary Representation http://numericalmethods.eng.usf.edu
http://numericalmethods.eng.usf.edu 3 How a Decimal Number is Represented 2 1 0 1 2 10 6 10 7 10 7 10 5 10 2 76 . 257 × + × + × + × + × =

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http://numericalmethods.eng.usf.edu 4 Base 2 1875 . 11 ) 2 1 2 1 2 0 2 0 ( ) 2 1 2 1 2 0 2 1 ( ) 0011 . 1011 ( 10 4 3 2 1 0 1 2 3 2 = × + × + × + × + × + × + × + × =
http://numericalmethods.eng.usf.edu 5 Convert Base 10 Integer to binary representation Table 1 Converting a base-10 integer to binary representation. Quotient Remainder 11/2 5 5/2 2 2/2 1 1/2 0 0 1 a = 1 1 a = 2 0 a = 3 1 a = Hence 2 2 0 1 2 3 10 ) 1011 ( ) ( ) 11 ( = = a a a a

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http://numericalmethods.eng.usf.edu 6 Start Input (N) 10 i = 0 Divide N by 2 to get quotient Q & remainder R a i = R Is Q = 0?
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