Finding similarities between binary strings

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I have been tasked with this puzzle for my programming class, it's purely a puzzle and doesn't count towards any grades, but not being able to solve it is really bugging me! We have been given two binary strings and have to find a pattern between the two:

First: 0011 1010 0001 0001 0111 1111

Second: 1001 0000 1111 0000 1000 0101

Both strings are 24 bits long, but the decimal conversions share no resemblance. I have tried breaking them down and looking for patterns, is it possible the binary should be reverse, should it be 4 bit wide decimals, hex??

E.g. should each 4 bit block be converted to decimal?

0011 1010 0001 0001 0111 1111

3 10 1 1 7 15

Or should it be 12 bits wide?

001110100001 000101111111

929 383

3A1 17F

I am completely stuck.

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I think one possible interpretation of the problem is "Find the longest common substring." (i.e., a string of 0s and 1s that appears in both is one form of a common pattern.)

But the way this problem is presented here, it's not obvious that that is the correct interpretation.