Decimal floating point number to binary

Decimal floating point number to binary is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Your task is to create a program that takes a decimal floating point number and displays its binary representation and vice-versa: takes a floating point binary number and outputs its decimal representation.
The output would be something like this:
23.34375 => 10111.01011
1011.11101 => 11.90625

J

In this draft, the task does not give any guidelines for handling precision. So we will use 99 places after the decimal point and trim any trailing zeros (and the decimal point, for integer case).

Also, since J does not have a "Decimal floating point number" data type, we will use a list of characters to represent a decimal or binary number (this corresponds roughly with the relevant feature set of REXX which seems to have had a strong influence on this draft of this task), and use internal (mantissa,exponent) representations during the conversion.

Implementation:

<lang J>b2b=:2 :0

 NB. string to rational number
 exp=. (1x+y i.'.')-#y
 mant=. n#.0"."0 y-.'.'
 number=. mant*n^exp*'.' e. y
 NB. rational number to string
 exp=. _99
 mant=. <.1r2+number*m^x:-exp
 s=. exp&(}.,'.',{.) (":m#.inv mant)-.' '
 ((exp-1)>.-+/*/\|.s e.'.0') }. s

)</lang>

Example use:

<lang J> 2 b2b 10 '23.34375' 10111.01011

  10 b2b 2 '1011.11101'

11.90625</lang>

REXX

This REXX version will handle any number of digits, with bases up to 242 (using extended ASCII characters).
Bases up to 62 will just use decimal digits along with upper and lowercase (Latin) letters.
This REXX program is a modified version of the original program which can handle any base (no limit),
and the original program did more extensive error checking.
This program handles numbers with leading signs   (-, +).
Bases that are negative are also supported   (which won't be explained here). <lang rexx>/*REXX programs converts any number in a base to another base; bases≤242*/ parse arg number toBase inBase digits . if toBase== | toBase==',' then toBase=10 /*Specified? No, use default*/ if inBase== | inBase==',' then inBase=10 /* " " " " */ if digits== | digits==',' then digits=60 /* */ if number== | number==',' then call err 'no number specified.' if \datatype(toBase,'W') then call err 'invalid toBase: ' toBase if \datatype(inBase,'W') then call err 'invalid inBase: ' inBase if \datatype(digits,'W') then call err 'invalid digits: ' digits numeric digits max(digits,length(number))+5 /*use a bigger numeric digs.*/ $=base(number,toBase,inBase) /*convert the number given. */ numeric digits digits /*use a smaller numeric digs*/ if toBase==10 then if pos('.',$)\==0 then $=format($) /*maybe use BIF*/ say number ' (in base' inBase") = " $ ' (in base' toBase")." exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────BASE subroutine─────────────────────*/ base: procedure; parse arg x 1 s 2 1 ox,tt,ii @#=0123456789; @abc='abcdefghijklmnopqrstuvwxyz'; @abcu=@abc; upper @abcu dontUse=@#'.+-'@abc || @abcu"0708090a0b0c0d"x; OK=@# || @abcu || @abc $=OK||space(translate(xrange('1'x,"fe"x),,dontUse),0) /*max base string.*/ m=length($)-1 /*"M" is the maximum base. */ if tt== then tt=10 /*assume base 10 if omitted.*/ if ii== then ii=10 /*assume base 10 if omitted.*/ i=abs(ii); t=abs(tt) if t==999 | t=="*" then t=m if t>m then call err 'invalid range for ToBase:' t"; the range is: " 2 m if i>m then call err 'invalid range for InBase:' i"; the range is: " 2 m !=substr($,1+10*(tt<0),t) /*character string for base.*/ if tt<0 then !=0 || ! /*prefix a zero if neg base.*/ if x== then return left(!,t) @=substr($, 1+10*(ii<0), i) /*@ =legal chars for base X.*/ oS= /*original sign placeholder.*/ if s='-' | s="+" then do /*process the sign (if any).*/

                      x=substr(x,2)        /*strip the sign character. */
                      oS=s                 /*save the original sign.   */
                      end

if (ii>10 & ii<37) | (ii<0 & ii>-27) then upper x /*uppercase it ? */ if pos('-',x)\==0 |, /*too many minus signs ? */

  pos('+',x)\==0 |,                        /*too many  plus signs ?    */
  x=='.'         |,                        /*is single decimal point ? */
  x==             then call err 'illegal number: ' ox

parse var x w '.' g /*sep whole from fraction. */ if pos('.',g)\==0 then call err 'illegal number: ' ox /*too many . */ items.1=0 /*# of whole part "digits". */ items.2=0 /*# of fractional "digits". */ __=w||g /*verify re-composed number.*/ _=verify(__,@'.') /*# have any unusual digits?*/ if _\==0 then call err 'illegal char in number:' ox 'char=' substr(__,_,1) if i\==10 then do /*convert # base I──►base 10*/

              _=0;  p=0                    /*convert the whole # part. */
                               do j=length(w)  to 1  by -1  while  w\==
                               _=_ + ((pos(substr(w,j,1),@)-1) * i**p)
                               p=p+1       /*increase power of the base*/
                               end   /*j*/
              w=_;  _=0;  p=1              /*convert fractional part.  */
                 do j=1 for length(g);_=_+((pos(substr(g,j,1),@)-1)/i**p)
                 p=p+1                     /*increase power of the base*/
                 end   /*j*/
              g=_
              end
         else if g\==  then g="."g       /*reinsert period if needed.*/

if t\==10 then do /*convert base10 # to base T*/

              if w\== then do            /*convert whole number part.*/
                                   do j=1;   _=t**j;   if _>w  then leave
                                   end   /*j*/
                             n=
                                 do k=j-1 to 1 by -1;   _=t**k;   d=w%_
                                 n=n || substr(!,1+d,1)
                                 w=w//_                 /*modulus = // */
                                 end     /*k*/
                             w=n||substr(!,1+w,1)
                             end
              if g\== then do;  n=       /*convert fractional part.  */
                                              do digits()+1  while g\==0
                                              p=g*t;    g=p//1;  d=p%1
                                              n=n || substr(!,d+1,1)
                                              end   /*digits()+1 ···*/
                             if n==0   then n=
                             if n\== then n='.'n   /*only a fraction?*/
                             g=n
                             end
              end

return oS || word(strip(space(w),'L',0)strip(strip(g,,0),"T",'.') 0,1) /*──────────────────────────────────ERR subroutine──────────────────────*/ err: say; say '***error!***: ' arg(1); say; exit 13</lang> output   when using the input of:   23.34375 2

23.34375  (in base 10)    =    10111.01011  (in base 2).

output   when using the input of:   1011.11101 10 2

1011.11101  (in base 2)    =    11.90625  (in base 10).

output   when using the input of:   3.14159265358979323846264338327950288419716939937510582097494 62

3.14159265358979323846264338327950288419716939937510582097494  (in base 10)    =    3.8mHUcirZ3g3aaX5Bn156eBkfOx43HPGx7xT3yBX1Aoh3TAAEolLiHWo8Z4XVLWesfA6  (in base 62).