A Simple Base 2 Example
Dr. Holly Hirst
Appalachian State University
The Shodor Education Foundation
June 1998
Let's look at a simple "computer."
- base is 2
- exponent range is -2 to 2
- number of bits in the mantissa is 3
What are all of the model numbers?
The possible exponents are:
The possible mantissas are:
Now let's list all of the numbers in order:
| Number | Base 10 Number | Gap | Relative Gap |
| 0 | 0 | |
| .100 x 2-2 | .125 | .125 | |
| .101 x 2-2 | .15625 | .03125 | .25 |
| .110 x 2-2 | .1875 | .03125 | .2 |
| .111 x 2-2 | .21875 | .03125 | .166667 |
| .100 x 2-1 | .25 | .03125 | .142857 |
| .101 x 2-1 | .3125 | .0625 | .25 |
| .110 x 2-1 | .375 | .0625 | .2 |
| .111 x 2-1 | .4375 | .0625 | .166667 |
| .100 x 20 | .5 | .0625 | .142857 |
| .101 x 20 | .625 | .125 | .25 |
| .110 x 20 | .75 | .125 | .2 |
| .111 x 20 | .875 | .125 | .166667 |
| .100 x 21 | 1 | .125 | .142857 |
| .101 x 21 | 1.25 | .25 | .25 |
| .110 x 21 | 1.5 | .25 | .2 |
| .111 x 21 | 1.75 | .25 | .166667 |
| .100 x 22 | 2 | .25 | .142857 |
| .101 x 22 | 2.5 | .5 | .25 |
| .110 x 22 | 3 | .5 | .2 |
| .111 x 22 | 3.5 | .5 | .166667 |
The Wilkinson Model of Arithmetic
Last update on: June 10, 1998
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