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 <=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 -> 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 -> 6 100101000 -> 73 1000000000 -> 89 1001000000100100010 -> 8432 1010000010001000100001010000 -> 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.