MGMT 1030 Chapter 10: MGMT 1030 Chapter 10 Notes
6 May 2018
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MGMT 1030 Chapter 10 Notes – Summary
Introduction
• The easiest way to align the two numbers is to shift the number with the smaller
exponent to the right a sufficient number of spaces to increase the exponent to match
the larger exponent.
• This process inserts insignificant zeros at the beginning of the number.
• Note that this process protects the precision of the result by maintaining all the digits of
the larger number.
• It is the least significant digits of the smaller number that will disappear.
• Once alignment is complete, addition or subtraction of the mantissas can take place.
• It is possible that the addition or subtraction may result in an overflow of the most
significant digit.
• In this case, the number must be shifted right and the exponent incremented to
accommodate the overflow.
• Otherwise, the exponent remains unchanged.
• It is useful to notice that the exponent can be manipulated directly in its excess form
• Since it is the difference in the two exponents that is of interest rather than the value of
the exponent itself.
• It is thus not necessary to change the exponents to their actual values in order to
perform addition or subtraction.
• EXAMPLE
• Add the two floating point numbers 05199520 04967850
• Assume that these numbers are formatted using sign-and-magnitude notation for the
mantissa and excess-50 notation for the exponent.
• The implied decimal point is at the beginning of the mantissa, and base 10 is used for
the exponent.
• Shifting the lower mantissa right two places to align the exponent, the two numbers
become 05199520 0510067850
