I notice that there is a syntax to enter a numeric literal in a different base, for example:

In[8]:= 5^^1000000000000101
Out[8]= 30517578151

However, there does not seem to be any function to enter a number in a different base. Since, it seems practically every operation in Mathematical has a corresponding function, this seems strange. Also, the documentation for ^^ is hidden in the BaseForm function's documentation, and is just barely mentioned. It is not listed as an operator at all.

This weird syntax is a problem for me. For example, I tried to display a number in different bases like this:

Map[(#^^1000000000000101) &, Range[2, 10]]

and it gives an error.


1 Answer 1


FromDigits can do the job:

FromDigits["1000000000000101", Range[2, 10]]

(* {32773, 14348917, 1073741841, 30517578151, 470184984613,
    4747561509993, 35184372088897, 205891132094731, 1000000000000101} *)
  • $\begingroup$ Yes, I knew about this command but it seemed like "cheating" because you are actually treating the number as a string. It does not actually handle the value numerically the way ^^ does. $\endgroup$ Apr 9, 2016 at 19:17
  • $\begingroup$ ^^ also treats the digits as a string even though syntactically it allows us to omit the quotes. Consider: 16^^face == FromDigits["face", 16]. $\endgroup$
    – WReach
    Apr 9, 2016 at 19:23
  • $\begingroup$ Or, with a number use FromDigits[IntegerDigits[1000000000000101], Range[2, 10]] $\endgroup$
    – Bob Hanlon
    Apr 9, 2016 at 20:16

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