diff --git a/notes/ANS Theory.md b/notes/ANS Theory.md index 68235e6..b8d8a79 100644 --- a/notes/ANS Theory.md +++ b/notes/ANS Theory.md @@ -31,7 +31,7 @@ To store two coin flips, you might have the first subdivision represent the outc | $0.25 - 0.5$ | Tails, Heads | | $0.50 - 0.75$ | Heads, Tails | | $0.75 - 1.00$ | Heads, Heads | -Imagine a situation where we want to store all possible outcomes of three consecutive coin flips *Heads, Heads, Tails*. +Imagine a situation where we want to store all possible outcomes of three consecutive coin flips using a decimal number, *Heads, Heads, Tails*. Encoding this would happen as follows: 1. First we subdivide the range by the probability of each event happening. The probability of each is 50%, so that's simple. Referring above, we know that heads is represented by the top half of the range, and tails is represented by the bottom half of the range. > Because the *first* coin flip resulted in *Heads*, the output value must be between $0.50$ and $1.00$. @@ -42,4 +42,5 @@ Encoding this would happen as follows: The decoding process performs the same series of steps, but by asking a question instead of outputting a value. 1. Is the value between $0.00$ and $0.50$? If so, the first coin flip resulted in *Tails*. Otherwise if the value is between $0.50$ and $1.00$, the first coin flip resulted in *Heads*. -The above process can be repeated just like the encoding process until we've determined the output of the first three \ No newline at end of file +The above process can be repeated just like the encoding process until we've determined the result of the first three coin flips. +