This is like a parody of mathematics.

There is no “final” element of an infinite series.

Computers can only perform a finite number of operations, so your computer programs aren't applicable at all.

Also: if you could count all the infinite binary strings, then "length" would be meaningless.

Take all the binaries between 0 and 1. Write them in a list. Then cover the first one with an interval of size ε/2, the second one with an interval of size ε/4, the third one with an interval of size ε/8, etc.

Now you've covered the whole unit line segment with a collection of interval whose sum is ε. But we can make ε as small as we like. This means the length of the unit line segment would be zero.