"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")

Note that 2^^ 1101 doesn't work either, which already is a strong hint that one shouldn't expect 2^^ # & to work. — celtschk, May 24 '12 at 12:12
I like how in MMA questions can appear to be censored curse words. What the F^^@@#? — yohbs, May 24 '12 at 13:24

score 12 · Accepted Answer · edited Apr 13 '17 at 12:55

12

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.

edited Apr 13 '17 at 12:55

Community

answered May 24 '12 at 10:57

Szabolcs

I feel that this previous question says it all. Vote to close this one? – Sjoerd C. de Vries May 24 '12 at 11:13
@Sjoerd Personally I'm fine with closing. Maybe the FromDigits part (how to actually construct that pure function) is a worthwhile addition here? – Szabolcs May 24 '12 at 11:16
Didn't we cover that here? – Sjoerd C. de Vries May 24 '12 at 11:49
@Sjoerd I did consider voting to close briefly, before posting an answer, but for some reason I didn't. Just do what you feel is correct :-) – Szabolcs May 24 '12 at 14:26
I wish I could just vote to close without casting a super close vote. I'm hesitating because of this pure function part in the question, but actually it doesn't make much of a difference. – Sjoerd C. de Vries May 24 '12 at 14:36

score 2 · Answer 2 · answered May 24 '12 at 13:48

2

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

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

answered May 24 '12 at 13:48

2 Answers2