MGMT 1030 Chapter Notes - Chapter 3: Decimal Mark
6 May 2018
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MGMT 1030 Chapter 3 Notes – Summary
Introduction
• Among the decisions made by the designer of the format are the number of digits to
use, the implied location of the binary or decimal point, the base of the exponent
• The method of handling the signs for the mantissa and the exponent.
• For example, suppose that the standard word consists of space for seven decimal digits
and a sign: SMMMMMMM
• This forat ould allo the storage of a iteger i the rage −9, 999, 999 < I < +99,
999, 999 with full, seven-digit precision.
• Numbers of magnitude larger than 9,999,999 result in overflow.
• Numbers of magnitude less than 1 cannot be represented at all, except as 0.
• For floating point numbers, we might assign the digits
• Sign of mantissa two digits for the exponent the remaining five digits for the mantissa
SEEMMMMM.
• In addition we have to specify the implied location for the decimal point.
• I this eaple e hae traded to digits of epoet i echage for the loss of two
digits of precision.
• We emphasize that we have not increased the number of values that can be
represented by seven digits.
• Seven digits can represent exactly 10,000,000 different values, no matter how they are
used.
• We have simply chosen to use those digits differently—to increase the expressible range
of values by giving up precision throughout the range.
• If we wish to increase the precision, one option is to increase the number of digits.
• There are other possible trades.
• We could, for example, increase precision by another digit by limiting the exponent to a
single digit.
• This might not be as limiting as it first appears.
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