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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. 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.