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Binary Representation

Binary Representation. Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker Presented by: A. Ranjbar http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Binary Representation http://numericalmethods.eng.usf.edu.

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Binary Representation

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  1. Binary Representation Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker Presented by: A. Ranjbar http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates http://numericalmethods.eng.usf.edu

  2. Binary Representationhttp://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu

  3. How a Decimal Number is Represented http://numericalmethods.eng.usf.edu

  4. Base 2 http://numericalmethods.eng.usf.edu

  5. Convert Base 10 Integer to binary representation Table 1 Converting a base-10 integer to binary representation. Hence http://numericalmethods.eng.usf.edu

  6. Start Input (N)10 Integer N to be converted to binary format i = 0 Divide N by 2 to get quotient Q & remainder R i=i+1,N=Q ai = R No Is Q = 0? Yes n = i (N)10 = (an. . .a0)2 STOP http://numericalmethods.eng.usf.edu

  7. Fractional Decimal Number to Binary Table 2. Converting a base-10 fraction to binary representation. Hence http://numericalmethods.eng.usf.edu

  8. Start Input (F)10 Fraction F to be converted to binary format Multiply F by 2 to get number before decimal, S and after decimal, T ai = R No Is T =0? Yes n = i (F)10 = (a-1. . .a-n)2 STOP http://numericalmethods.eng.usf.edu

  9. Decimal Number to Binary Since and we have http://numericalmethods.eng.usf.edu

  10. All Fractional Decimal Numbers Cannot be Represented Exactly Table 3. Converting a base-10 fraction to approximate binary representation. http://numericalmethods.eng.usf.edu

  11. Another Way to Look at Conversion Convert to base 2 http://numericalmethods.eng.usf.edu

  12. http://numericalmethods.eng.usf.edu

  13. Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://numericalmethods.eng.usf.edu/topics/binary_representation.html http://numericalmethods.eng.usf.edu

  14. THE END http://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu

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