Re: Inverse of IntegerDigits? and "Index" function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg3956] Re: Inverse of IntegerDigits? and "Index" function?*From*: Paul Abbott <paul at earwax.pd.uwa.edu.au>*Date*: Sat, 11 May 1996 23:53:09 -0400*Organization*: University of Western Australia*Sender*: owner-wri-mathgroup at wolfram.com

pehowland at taz.dra.hmg.gb wrote: > Inverse of IntegerDigits > ======================== > I'm playing around with some binary numbers, and am using > IntegerDigits > to convert from a decimal integer to the binary notation. eg. > In[1]:= IntegerDigits[10,2] > Out[1]= {1,0,1,0} > > What is the function to convert back? eg. I want to do > In[2]:= DigitsToInteger[{1,0,1,0},2] > and get > Out[2]= 10 Have a look at the Mathematica Journal 2(2):35: Horner[u_List, base_] := Fold[base #1 + #2 &, 0, u] Horner[{1,0,1,0},2] 10 > "Index" Function > ================ > Writing a function to convert back is easy in principle, eg. > > DigitsToInteger[x_,n_] := Apply[Plus[Map[(#*n^(Index[#]-1))&, Reverse[x]]]] > > would do the trick, but I seem to require a function, that I've called > Index[] here, that when Map[]'d across a list returns the position of > each element. Thus I want a function that works as follows: > > In[3]:= Map[Index[#]&, {2,6,3,9,10,2,4}] > Out[3]= {1,2,3,4,5,6,7} Try MapIndexed: ?MapIndexed MapIndexed[f, expr] applies f to the elements of expr, giving the part specification of each element as a second argument to f. MapIndexed[f, expr, levspec] applies f to all parts of expr on levels specified by levspec. MapIndexed[f, {2,6,3,9,10,2,4}] {f[2, {1}], f[6, {2}], f[3, {3}], f[9, {4}], f[10, {5}], f[2, {6}], f[4, {7}]} MapIndexed[#2 &, {2,6,3,9,10,2,4}] {{1}, {2}, {3}, {4}, {5}, {6}, {7}} Cheers, Paul _________________________________________________________________ Paul Abbott Department of Physics Phone: +61-9-380-2734 The University of Western Australia Fax: +61-9-380-1014 Nedlands WA 6907 paul at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/Paul _________________________________________________________________ ==== [MESSAGE SEPARATOR] ====