Fibonacci coding

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The Fibonacci code is a universal code which encodes positive integers into binary code words. All tokens end with "11" and have no "11" before the end. The code begins as follows:

1  11
2  011
3  0011
4  1011
5  00011
6  10011
7  01011
8  000011
9  100011
10 010011
11 001011
12 101011

To encode an integer X:

1. Find the largest Fibonacci number equal to or less than X; subtract this number from X, keeping track of the remainder.
2. If the number we subtracted was the Nth Fibonacci number, put a one in the Nth digit of our output.
3. Repeat the previous steps, substituting our remainder for X, until we reach a remainder of 0.
4. Place a one after the last naturally-occurring one in our output.

To decode a token in the code, remove the last "1", assign the remaining bits the values 1,2,3,5,8,13... (the Fibonacci numbers), and add the "1" bits.