Do bitwise operators (other than shifts) make any mathematical sense in base-10?

In that case, yes, they can be extended to base-10 in several ways, though they aren't nearly as useful as in binary.

Yes, there are other useful operations, but they tend to be oriented towards operations involving powers of 2 (for obvious reasons), e.g. Test for odd/even, test for power of 2, round up/down to nearest power of 2, etc.

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