Re: converting a number in base b to a number in base 10 using ^^ in Mathematica

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Re: converting a number in base b to a number in base 10 using ^^ in Mathematica*From*: David Withoff <withoff>*Date*: Thu, 26 Mar 1992 16:37:12 -0600

In response to Prof. Gaylord's note: > base2tobase10conversion[n_Integer] := 2^^n > General::digit: > Digit at position 1 in n > is too large to be used in > base 2. > > it seems that the ^^ operator absolutely insists on being immediately > followed by an integer. > > can someone suggest another way (there must be; there's always another way > to do almost everything in M) to convert a number in base b to base 10 > other than using ^^. > > i find it hard to believe that M does not have a built-in function for > doing this but i can't find it in the book. You could do something like this: In[4]:= c[n_] := ToExpression[StringJoin["2^^", ToString[n]]] In[5]:= c[101] Out[5]= 5 The ^^ operation is one of a very small number of operations (the other ones being things like ??) that are handled by the parser rather than the evaluator. One difficulty with implementing ^^ as a separate function is handling of bases greater than 10: In[6]:= 16^^3fa7 Out[6]= 16295 If 3fa7 appeared as a function argument it would be parsed as Times[3, fa7] rather than as a string of characters, and it seems a bit awkward to have to enter a number as a string in the first place. I was a bit surprised myself when I first realized that there wasn't a built-in function to do this, and if not for pesky design issues (like how to handle bases bigger than 10) there probably would be. Dave Withoff withoff at wri.com