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