Fitting a discrete binning structure to a continuous binning structure

I have two binning structures, one is discrete which has gaps in between and different lengths and the one with continuous bins, no gap and same lengths.

|---|   |-----| |---|      |--|    |----------|

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |

How can I resort the data from the discrete bins to the continuous bins? Thanks

[Bruno Pop-Stefanov]

Can you explain your problem a bit more? What are those bins and what do they contain?