Converting a number from Zeckendorf Representation to Decimal About Zeckendorf Representations/Base Fibonacci Numbers

This is a number system which uses Fibonacci numbers as its base. The numbers consist of 0 and 1's and each 1 means that the number contains the corresponding Fibonacci number, and 0 means it does not.

For example, let's convert all natural numbers &lt;=10 to base Fibonacci.


1 will become 1, because it is the sum of 1, which is a Fibonacci number,
2 will become 10, because it is the sum of 2, which is a Fibonacci number, and it does not need 1, because we already achieved the desired sum.
3 will become 100, because it is the sum of 3, which is a Fibonacci number and it does not need 2 or 1 because we already achieved the desired sum.
4 will become 101, because it is the sum of [3,1], both of which are Fibonacci numbers.
5 will become 1000, because it is the sum of 5, which is a Fibonacci number, and we do not need any of the other numbers.
6 will become 1001, because it is the sum of the Fibonacci numbers 5 and 1.
7 will become 1010, because it is the sum of the Fibonacci numbers 5 and 2.
8 will become 10000, because it is a Fibonacci number.
9 will become 10001, because it is the sum of the Fibonacci numbers 8 and 1.
10 will become 10010, because it is the sum of the Fibonacci numbers 8 and 2.


Let's convert a random Base Fibonacci number, 10101001010 to decimal:
First we write the corresponding Fibonacci numbers.
Then we compute the sum of the numbers under 1's.

 1   0   1   0   1   0   0   1   0   1   0
 144 89  55  34  21  13  8   5   3   2   1  -&gt; 144+55+21+5+2 = 227.


Read more about Base Fibonacci numbers: link, it also has a tool which converts regular integers to base Fibonacci. You can experiment with it.

Now the Question:

Your task is to take a number in the Zeckendorf Representation, and output its decimal value.

Input is a string which contains only 0 and 1's (although you can take the input in any way you want).

Output one number in decimal.

Test cases: (in the format input->output)

 1001 -&gt; 6
 100101000 -&gt; 73
 1000000000 -&gt; 89
 1001000000100100010 -&gt; 8432
 1010000010001000100001010000 -&gt; 723452


This is code-golf, so the shortest answer in bytes wins.

Note: The input will not contain any leading 0's or consecutive 1's.
Taxi, 1987 1927 bytes

-60 bytes due to the realization that linebreaks are optional.

Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to Chop Suey.Go to Chop Suey:n 1 r 1 l 4 r 1 l.[B]Switch to plan C if no one is waiting.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 3 l.Pickup a passenger going to Narrow Path Park.Pickup a passenger going to Sunny Skies Park.Go to Zoom Zoom:n.Go to Sunny Skies Park:w 2 l.Go to Narrow Path Park:n 1 r 1 r 1 l 1 r.Go to Chop Suey:e 1 r 1 l 1 r.Switch to plan B.[C]1 is waiting at Starchild Numerology.1 is waiting at Starchild Numerology.Go to Starchild Numerology:n 1 l 3 l 3 l 2 r.Pickup a passenger going to Addition Alley.Pickup a passenger going to Cyclone.Go to Cyclone:w 1 r 4 l.[D]Pickup a passenger going to Addition Alley.Pickup a passenger going to Cyclone.Go to Addition Alley:n 2 r 1 r.Go to Cyclone:n 1 l 1 l.Pickup a passenger going to Multiplication Station.Go to Zoom Zoom:n.Go to Narrow Path Park:w 1 l 1 l 1 r.Switch to plan E if no one is waiting.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:e 1 r.Pickup a passenger going to Multiplication Station.Go to Multiplication Station:n 1 r 2 l.Pickup a passenger going to Joyless Park.Go to Joyless Park:n 2 l 1 r 1 r.Go to Addition Alley:w 1 r 2 l 1 l.Pickup a passenger going to Cyclone.Go to Cyclone:n 1 l 1 l.Pickup a passenger going to Addition Alley.Switch to plan D.[E]Go to Addition Alley:w 1 l 1 r 1 l.Pickup a passenger going to Riverview Bridge.Go to Riverview Bridge:n 1 r.Go to Joyless Park:e 1 r 2 l.Pickup a passenger going to Addition Alley.[F]Switch to plan G if no one is waiting.Pickup a passenger going to Addition Alley.Go to Fueler Up:w 1 l.Go to Addition Alley:n 3 l 1 l.Pickup a passenger going to Addition Alley.Go to Joyless Park:n 1 r 1 r 2 l.Switch to plan F.[G]Go to Addition Alley:w 1 r 2 l 1 l.Pickup a passenger going to The Babelfishery.Go to The Babelfishery:n 1 r 1 r.Pickup a passenger going to Post Office.Go to Post Office:n 1 l 1 r.


Try it online!

Because I don't return to the Taxi Garage at the end, my boss fires me, so it exits with an error.