"A number in base b" and pure functions: why doesn't b^^# & work?

Question

Why do the following not work (in Mathematica 7)?

2^^ # & /@ {1000, 1101}

and

2^^ # & @ 1101

This does work:

2^^1101

giving, as expected:

(*13*)

(This also works:

BaseForm[#, 2] & /@ {13, 14}

)

See here for further information ("Digits in numbers")

Answer 1

The reason is that the notation base^^digits is interpreted at parsing time, not evaluation time. I explained the difference in this answer.

You can use FromDigits instead:

fromBaseTwo = FromDigits[#, 2]& 

fromBaseTwo["10011"]

Note that I used a string as input. FromDigits works both with strings and lists of digits.

Answer 2

Here is a somewhat messed-up way to do something like what you wanted to do:

ToExpression["2^^" <> ToString[#]] & /@ {1000, 1101}
{8, 13}