MGMT 1030 Chapter Notes - Chapter 16: Radix Point
6 May 2018
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MGMT 1030 Chapter 16 Notes – Summary
Introduction
• To the left of the radix point, the multipliers are integer, and there is a direct
relationship between the different bases.
• To the right of the point, the multipliers are fractional
• There may or may not be a rational relationship between the multipliers in the different
bases.
• The solution is to convert each side of the radix point separately using the techniques
discussed
• As an alternative, you can multiply the entire number in one base by whatever number
is required to make the entire number an integer
• Then convert the number in integer form.
• When this is complete, however, you must divide the converted result by that same
multiplier in the new base.
• It is not correct to simply shift the radix point back, since each shift has a different value
in the new base!
• Thus, if you shift a binary point right by seven places, you have effectively multiplied the
number by 128.
• You must divide the converted number by 128 in the new base.
• This latter method is best illustrated with an example.
• EXAMPLE
• Convert the decimal number 253.75 to binary floating point form.
• Begin by multiplying the number by 100 to form the integer value 25375.
• This is converted to its binary equivalent 110001100011111, or 1.10001100011111 ×
214.
• The IEEE 754 floating point equivalent representation for this integer would be 0
• Sign Excess-127 Exponent = 127 + 14
• Mantissa (initial 1 is dropped) 10001101 10001100011111
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