MGMT 1030 Chapter Notes - Chapter 5: Decimal Mark
6 May 2018
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MGMT 1030 Chapter 5 Notes – Summary
Introduction
• It is simpler to use for exponents than the complementary form, and appropriate to the
calculations required on exponents.
• In our example we have used excess-50 notation.
• This allos us to stoe a epoetial age of − to +9, oespodig to the stoed
values 00 to 99.
• We could, if we wished, pick a different offset value, which would expand our ability to
handle larger numbers at the expense of smaller numbers, or vice versa.
• If we assume that the implied decimal point is located at the beginning of the five-digit
mantissa, excess- otatio allos us a agitude age of . × − < ue
< 0.99999 × 10+49
• This is an obviously much larger range than those possible using integers
• At the same time gives us the ability to express decimal fractions.
• In practice, the range may be slightly more restricted, since many format designs require
that the most significant digit not be 0, even for very small numbers.
• I this ase, the sallest epessile ue eoes . × −, ot a geat
limitation.
• The word consisting of all 0s is frequently reserved to represent the special value 0.0.
• If we were to pick a larger (or smaller) value for the offset, we could skew the range to
store smaller (or larger) numbers.
• Generally, values somewhere in the midrange seem to satisfy the majority of users, and
there seems little reason to choose any other offset value.
• Notice that, like the integer, it is still possible, although very difficult, to create an
overflow by using a number of magnitude too large to be stored.
• With floating point numbers it is also possible to have underflow
• Where the number is a decimal fraction of magnitude too small to be stored.
• The diagram shows the regions of underflow and overflow for our example.
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