MGMT 1000 Lecture 21: MGMT 1000 Lecture 21 Notes
MGMT 1000 Lecture 21 Notes – Fractional Conversion Methods
Introduction
• The converse is not the case
• Since all fractions of the form 1/2k can be represented in base 10, and since each bit
represents a fraction of this form, fractions in base 2 can always be converted exactly to
fractions in base 10.
• As we have already shown with the value 0.110, many base 10 fractions result in endless
base 2 fractions.
• Incidentally, as review, consider the hexadecimal representation of the binary fraction
representing 0.110.
• Starting from the numeric point, which is the common element of all number bases (B0
=1 in all bases), you group the bits into groups of four
o 1001 1001 1001 = 0.1999916
• In this particular case, the repeat cycle of four happens to be the same as the
hexadecial groupig of four, so the digit 9 repeats forever.
• When fractional conversions from one base to another are performed, they are simply
stopped when the desired accuracy is attained (unless, of course, a rational solution
exists).
• The intuitive conversion methods previously discussed can be used with fractional
numbers.
• The computational methods have to be modified somewhat to work with fractional
numbers.
• Consider the intuitive methods first.
• The easiest way to convert a fractional number from some base B to base 10 is to
determine the appropriate weights for each digit, multiply each digit by its weight, and
add the values.
• You will note that this is identical to the method that we introduced previously for
integer conversion.
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