Fitting a discrete binning structure to a continuous binning structure

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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

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