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

• To: mathgroup at smc.vnet.net
• Subject: [mg3966] Re: Inverse of IntegerDigits? and "Index" function?
• From: danl (Daniel Lichtblau)
• Date: Mon, 13 May 1996 01:46:55 -0400
• Organization: Wolfram Research, Inc.
• Sender: owner-wri-mathgroup at wolfram.com

```In article <4menl1\$jva at dragonfly.wolfram.com> pehowland at taz.dra.hmg.gb ()
writes:
>
> 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
>
=========================================================================
>

Here are a couple of methods. The first is along the lines of your first
attempt, the second is a more list-oriented way of doing the Hornering of
your second method.

In[13]:= DigitsToInteger1[x_List, base_Integer] := x.Table[base^k,
{k,Length[x]-1,0,-1}]

In[14]:= DigitsToInteger2[x_List, base_Integer] := Fold[(base*#1 + #2)&,
0, x]

In[15]:= DigitsToInteger1[{1,0,1,0},2]
Out[15]= 10

In[16]:= DigitsToInteger2[{1,0,1,0},2]
Out[16]= 10

Daniel Lichtblau
Wolfram Research, Inc.
danl at wolfram.com

==== [MESSAGE SEPARATOR] ====

```

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