That could be possible, you could even do it today, if you wanted:

    macro operator binary ^$
      ASTE $left bitxor $right

There are also operators for `and`, `or`, `xor` which act logically. `not` which does a boolean invert. So there are `bitand`, `bitor`, `bitxor`, `bitnot` which fit well as working bitwise instead of logically.

I suppose the outliers are `bitlshift`, `bitrshift`, `biturshift`, but it does somewhat make sense to keep the `bit` prefix because it casts to int32 and because its operations are inherently bitwise.