How to find the nth binary permutation?

[fredreload]

This is the last missing piece I need to complete my compression algorithm, new one. Let's say I have 4 bits with 2 bits set as 1, 0011. The total number of permutations for this number is 0011, 0101, 0110, 1001, 1010, 1100, 6 cases. This can be computed using the calculation.

 

4! / ((2!)(4-2)!) = 6

 

Now I want to be able to find the nth sequence, for instance 1st number is 0011, second number is 0101. So if I say n=5, I want to be able to get the 5th permutation sequence 1010 from the initial 0011. How do I do this?

[mathematic]

You need to define how the permutations are ordered. Permutations give you a total, but they can be in any order.

[fredreload]

Right as I've mentioned I want 0011 to be 1, so having all the one bits on the right as 1, then slowly move to the left. It really doesn't matter as long as I can track the sequence in an orderly fashion. So I want to be able to derive a sequence using the nth value. For instance I want n=5 to get me 1010 in this case

 

P.S. We know how we can get any binary order using 2 to the power, for instance if I have n=15 I would get 15-2^3-2^2-2^1-2^0 and get 1111

Edited October 1, 2016 by fredreload

[Strange]

You can find several discussions of this on Stack Overflow and elsewhere. For example:
http://stackoverflow.com/questions/7918806/finding-n-th-permutation-without-computing-others
http://math.stackexchange.com/questions/60742/finding-the-n-th-lexicographic-permutation-of-a-string
http://stackoverflow.com/questions/29236556/how-can-i-calculate-n-th-permutation-or-tell-the-lexicographic-order-of-a-given
https://codesciencelove.wordpress.com/2013/07/15/finding-the-nth-lexicographic-permutation-of-0123456789/
https://apps.topcoder.com/forums/?module=Thread&threadID=645384
https://www.quora.com/How-can-we-find-the-lexicographically-Kth-permutation-of-the-sequence-1-N-efficiently
http://nrecursions.blogspot.co.uk/2014/02/nth-permutation-without-swapping.html
http://code.activestate.com/recipes/126037-getting-nth-permutation-of-a-sequence/
http://www.confusedcoders.com/data-structures/lexicographic-permutation-of-string
http://echochamber.me/viewtopic.php?t=104500

That is just the first page of results for: https://www.google.com/search?q=generating+nth+permutation

[AshBox]

You can also find your answer in this link:

 

http://binarytranslator.com/