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notes/ANS Theory.md
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@ -31,7 +31,7 @@ To store two coin flips, you might have the first subdivision represent the outc
| $0.25 - 0.5$ | Tails, Heads | | $0.25 - 0.5$ | Tails, Heads |
| $0.50 - 0.75$ | Heads, Tails | | $0.50 - 0.75$ | Heads, Tails |
| $0.75 - 1.00$ | Heads, Heads | | $0.75 - 1.00$ | 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: 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. 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 $1.00$. > 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. 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*. 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 The above process can be repeated just like the encoding process until we've determined the result of the first three coin flips.