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notes/ANS Theory.md
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@ -6,4 +6,6 @@ This makes the amount of information a single digit stores *uniform* across all
ANS theory is based around the idea that digits that occur more often can be stored in a way that requires less information, and digits that occur less often can be stored using more information.
Taking a look at the standard binary numeral system, there are two digits in the set (0 and 1). Given a natural number represented in binary, eg `1010`, there are two different ways to *add information to that number*
Taking a look at the standard binary numeral system, there are two digits in the set (0 and 1). Given a natural number represented in binary, eg `1010`, there are two different ways to *add information to that number*:
1. We can add a digit to the most significant position. As an example, adding a `1` to the above value would result in `11010`. Doing this means that the added digit stores information about *large ranges*. In the provided example, this means that setting that digit changes the value by 16.
2. We can add a digit to the least significant position. As an example, adding a `1` to the above value would result in `10101`. Changing the added digit will only change the value by 16.