MGMT 1030 Lecture Notes - Lecture 32: Radix, Microsoft Excel
6 May 2018
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MGMT 1030 Lecture 32 Notes – Te’s copleet
Introduction
• The positive range limit for 16 bits is +32767 (a 0 for the sign plus fifteen 1s
• Since the sum of 16384 and 16386 is 32770, the calculation overflows.
• Unfortunately, the user may never notice, especially if the overflowing calculation is
buried in a long series of calculations.
• A good programmer takes such possibilities into account when the program is written.
• This type of error caused some embarrassment when it showed up in a recent version of
Microsoft Excel.
• You have seen that complementary representation can be effective for the
representation and calculation of signed integer numbers.
• As you are also aware, the system that we have described, which uses the largest
number in the base as its complementary reflection point
• Suffers from some disadvantages that result from the dual zero on its scale.
• By shifting the negative scale to the right by one, we can create a complementary
system that has only a single zero.
• This is done by using the radix as a basis for the complementary operation.
• I deial ase, this is kow as the ’s opleet epesetatio.
• The use of this representation will simplify calculations.
• The trade-off i usig ’s opleet epesetatio is that it is slightly more difficult
to find the complement of a number.
• A three-digit decimal scale is shown
• Be sure to notice the differences between these diagrams
• The theoy ad fudaetal tehiue fo ’s opleet is the sae as that fo 9’s
complement.
• The ’s opleet epesetatio uses the odulus as its efletio poit.
• The modulus for a three-digit decimal representation is 1000, which is one larger than
the largest number in the system, 999.
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