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MathGroup Archive 1996

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Inverse of IntegerDigits? and "Index" function?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3922] Inverse of IntegerDigits? and "Index" function?
  • From: pehowland at taz.dra.hmg.gb ()
  • Date: Fri, 10 May 1996 03:28:20 -0400
  • Organization: LSC2 Division, Defence Research Agency
  • Sender: owner-wri-mathgroup at wolfram.com

Excuse me if I'm being particularly inept this morning, but can anyone offer
any help on the following problems please?

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
I've scoured the manual and can't find the function.  This led me to
try to write my own function, which identified another problem...

"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}

But I can't seem to find this function either!

For the moment I'm using the following more Fortran-like function, which
works, but disturbs my sensibilities:
 
 DigitsToInteger[x_,n_] :=
    Module[{int=0, l},
            l = Reverse[x];
            Do  [int = int + 2^(i-1)*l[[i]],
                 {i, Length[i]}
                ];
            int
          ]


Any suggestions?

Paul E Howland                                  Tel. +44 (0)1684 895767
Long Range Ground Radar Sensors                 Fax. +44 (0)1684 896315
LSC2 Division                                 Email. PEHOWLAND at DRA.HMG.GB
Defence Research Agency
St Andrews Road
Malvern
Worcestershire, WR14 3PS, UK
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