I don’t think it really makes sense in the binary context. If there are only two possible values (0 and 1), then you’ll have so many ties and also you won’t be able to get meaningful quadruples. I think the closest analogue in the binary context is probably mutual information, although this is clearly measuring a different thing.
Although, I guess you could theoretically try taking the values in each sequence in groups of N at a time and then interpreting each grouping of binary digits as an integer, and then compute the Hoeffding’s D of the resulting integers. Maybe doing that for a range of N values, like 3 to 8, and averaging the Hoeffding’s D values you get. Not sure if that really makes sense though, I need to try it with some real data!
Although, I guess you could theoretically try taking the values in each sequence in groups of N at a time and then interpreting each grouping of binary digits as an integer, and then compute the Hoeffding’s D of the resulting integers. Maybe doing that for a range of N values, like 3 to 8, and averaging the Hoeffding’s D values you get. Not sure if that really makes sense though, I need to try it with some real data!