diff --git a/notes/ANS Theory.md b/notes/ANS Theory.md
index 84ebb58..0c70945 100644
--- a/notes/ANS Theory.md	
+++ b/notes/ANS Theory.md	
@@ -13,4 +13,8 @@ Taking a look at the standard binary numeral system, there are two digits in the
 Given that $x$ represents a natural number, and $s$ is the digit we're adding. In a standard binary system, adding $s$ to the least significant position means that in the new number $x$ (before the addition) now represents the Nth appearance of an even (when $s = 0$ ), or odd (when $s = 1$). With ANS, the goal is is to make that asymmetrical, so that you can represent more common values with a denser representation.
 
 # Arithmetic Coding
-Arithmetic coding works 
+Arithmetic coding works by taking a stream of data, and converting it into an infinitely precise number between $0.00$, and $1.00$. This is based off of the idea that the sum of the probability of all events happening will always amount to $100\%$. 
+
+For example, the probability of a coin flip resulting in tails is 50%, and the probability of a coin flip resulting in heads is 50%. The probability of a coin flip resulting in heads *or* tails is %100.
+
+If we wanted to keep track of the result of a series of coin flips, this could be done by subdividing a range. If the coin flip is between $0$ and $0.5$, then we know that the first flip must