MGMT 1030 Chapter Notes - Chapter 11: Decimal Mark
6 May 2018
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MGMT 1030 Chapter 11 Notes – Summary
Introduction
Multiplication and division
• We must again shift the mantissa right one place and increment the exponent to
accommodate this digit: 05210019(850)
• Rounding the result to five places of precision, we finally get 05210020.
• Checking the result, = . × = . = . × − =
0.06785 10.01985 = 0.1001985 × 102 which converts to the result that we previously
obtained.
• Alignment is not necessary in order to perform multiplication or division.
• Exponential numbers are multiplied (or divided) by multiplying (dividing) the two
mantissas and adding (subtracting) the two exponents.
• The sign is dealt with separately in the usual way.
• This procedure is relatively straightforward.
• There are two special considerations that must be handled, however
• Multiplication or division frequently results in a shifting of the decimal point (e.g., 0.2 ×
0.2 = 0.04)
• Normalization must be performed to restore the location of the decimal point and to
maintain the precision of the result.
• We must adjust the excess value of the resulting exponent.
• Adding two exponents, each of which contains an excess value, results in adding the
excess value to itself
• So the final exponent must be adjusted by subtracting the excess value from the result.
• Similarly, when we subtract the exponents, we subtract the excess value from itself, and
we must restore the excess value by adding it to the result.
• EXAMPLE
• This is seen easily with an example. Assume we have two numbers with exponent
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