wpe41.gif (23084 bytes)CIS3355: Business Data Structures
Fall, 2008
 

What is more important: precision or magnitude ??

Once again, that depends on what values you are trying to store:

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Atoms in a jar (magnitude)

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The value of pi (precision)

However, we need to think about this in terms of general usage, and how much the addition of affects either precision or magnitude.

Let's assume that we wish to be able to represent all mantissa's to 5 decimal point of precision:

Bits available  Maximum Value Level of Precision
13 213 = 8,192 3
14 214 = 16,389 4
15 215 = 32,768 4
16 215 = 65,536 4
17 215 = 131,072 5

We need to allocate 17 bits to the mantissa in order to have 5 decimals of precision (remember: even though 215 = 131,072 and there are 6-digits in the value 131,072 we can not represent all 6 digit values with 15 buts, but we can represent ALL 5 digit values).

However, suppose that we wished to be able to represent all characteristic of exponent values to 5 digits (remember that the characteristic of the exponent can take on either negative or non-negative values:

Bits available  Maximum Value Exponent Range
2 -22  to +22  - 1 -4 to +3
3 -23  to +23  - 1 -8 to +7

In other words, we need to allocate fewer bits to the characteristic of the exponent to obtain a greater range of values.

How are bits distributed between each of the real number components?

That is our next tutorial.

This page was last updated on 05/31/05