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I want to convert a hexadecimal string to a decimal (base 10) number:

16^^ff
16^^ToExpression["ff"]

The 1st line returns the correct answer of 255, while the 2nd line gives an error. Why doesn't it work?

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    $\begingroup$ It is not correct to say (or, rather, imply) that the sigil ^^ corresponds to BaseForm, although I grant you that this is referenced in the BaseForm documentation. It is just another notation for entering numbers, like 1*^10. These particular notations are processed by the parser, are not interpreted as functions, and require that numeric literals appear both on the left and the right. It doesn't work since ToExpression["ff"] is not a numeric literal. You may use e.g. ToExpression@ToString@StringForm["16^^``", "ff"] instead. $\endgroup$ – Oleksandr R. Feb 2 '14 at 18:09
  • $\begingroup$ Oleksandr, What do the two grave accents mean in this case? I've seen them before to indicate accuracy, as in Accuracy[1.2``20] $\endgroup$ – DavidC Feb 2 '14 at 18:21
  • $\begingroup$ @DavidCarraher It is just StringForm's syntax... The second argument to StringForm gets inserted where ever there's a double backtick. If you have more than one argument to insert, you can indicate the order with a number, like `1`. $\endgroup$ – rm -rf Feb 2 '14 at 18:28
  • $\begingroup$ See here: mathematica.stackexchange.com/a/39753/4346 $\endgroup$ – Chip Hurst Feb 2 '14 at 19:42
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    $\begingroup$ Perhaps you have good reasons to use ToExpression but FYI the usual method to interpret a hexadecimal string is with FromDigits, e.g. FromDigits["FF", 16] gives 255 $\endgroup$ – Simon Woods Feb 2 '14 at 20:56
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As already stated in the comments the ^^ notation is handled in parsing; observe:

HoldComplete[16^^ff] // FullForm
HoldComplete[255]

(I intend this to illustrate that this notation is "evaluated" before the main evaluator ever sees it.)

This parsing is really no different from other numerical notation in Mathematica, for example 12.345 is directly parsed as a Real number, not an expression involving Dot. Likewise 1*^6 is parsed as the Integer one million, with no relation to Times or Power.

As Simon Woods recommended, for programmatic input of hexadecimals use FromDigits:

FromDigits["ff", 16]
255
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