# Mathematical Information Loss Posted on by James Thomas.

Reciprocal Distribution, Hamming, Mathematical Information Loss

#### Rounding

If you are looking for basic understanding of rounding in a computational context, check out this article from the EE times. While that’s a good starting point, I’m going to expand on this particular topic and look at the issues that arise from information loss.

#### Mantissas

Computers use a discrete number system. The mantissa of the number in binary can only represent a certain number of fractions because the digits are limited. Due to the rounding, overflow, and subnormal numbers created from arithmetic on these sets of numbers, we see the reciprocal distribution in the data sets of the mantissas.

#### The Reciprocal Distribution

In probability and statistics when you do arithmetic on distributions that contain a limiting distribution, the outcomes and feedback will be restrained to this distribution. In the case of computers, arithmetic between distributions naturally tend toward a reciprocal distribution.

#### How to Solve the Problems

While the solutions for these problems are complex and I have not yet finished Hamming’s book, there will most likely not be one correct answer to a particular solution. However, you will have to understand the problem intuitively and be able to manipulate the equations you are using to reduce the errors in calculations and so far the book has done an excellent job at that.