Non-decimal radices/Convert

From Rosetta Code
Task
Non-decimal radices/Convert
You are encouraged to solve this task according to the task description, using any language you may know.

Number base conversion is when you express a stored integer in an integer base, such as in octal (base 8) or binary (base 2). It also is involved when you take a string representing a number in a given base and convert it to the stored integer form. Normally, a stored integer is in binary, but that's typically invisible to the user, who normally enters or sees stored integers as decimal.


Task

Write a function (or identify the built-in function) which is passed a non-negative integer to convert, and another integer representing the base.

It should return a string containing the digits of the resulting number, without leading zeros except for the number   0   itself.

For the digits beyond 9, one should use the lowercase English alphabet, where the digit   a = 9+1,   b = a+1,   etc.

For example:   the decimal number   26   expressed in base   16   would be   1a.

Write a second function which is passed a string and an integer base, and it returns an integer representing that string interpreted in that base.

The programs may be limited by the word size or other such constraint of a given language. There is no need to do error checking for negatives, bases less than 2, or inappropriate digits.

11l

Converting from string to number:

print(Int(‘1A’, radix' 16)) // prints the integer 26

Converting from number to string:

print(String(26, radix' 16)) // prints ‘1A’

8086 Assembly

Be it a bug or otherwise "unintended" behavior, the AAD instruction, which was meant to convert unpacked binary-coded decimal values to hex to allow for division, has a "secret" operand that most assemblers did not support at the time. Typing AAD into your assembler would place the hex values D5 0A in your program. The 0A (hexadecimal equivalent of decimal 10) actually represents the base, and can be used to convert between bases in a roundabout way. Unpacked binary-coded decimal (also known as ASCII binary coded decimal) only uses the bottom four bits of each byte, so for example a number like 0x0103 represents decimal 13.

mov ah,02h
mov al,00h     ;this is the unpacked encoding of octal "20" aka 10 in hexadecimal, 16 in decimal. Ignore the leading zeroes.
byte 0D5h,08h  ;most assemblers don't allow you to encode a base so we have to inline the bytecode.

The result is that AX now equals 0x0010.

The AAM instruction (ASCII Adjust for Multiplication) has a similar "feature." You'll need to inline the bytecode D4 ?? where ?? is your desired base. These two can be used in combination to switch from hexadecimal to binary coded decimal without needing a lookup table or multiplication.

mov ax,10h
aam
byte 0D5h,10h  ;inlined bytecode for AAD using base 16

The result is that AX = 0x0016. This effectively lets us convert a hexadecimal value to one that "looks like" its decimal equivalent, albeit the logic only holds for 8-bit values. (This is a useful technique for printing numbers to the screen in decimal.)

ACL2

(defun digit-value (chr)
   (cond ((and (char>= chr #\0)
               (char<= chr #\9))
          (- (char-code chr) (char-code #\0)))
         ((and (char>= chr #\A)
               (char<= chr #\Z))
          (+ (- (char-code chr) (char-code #\A)) 10))
         ((and (char>= chr #\a)
               (char<= chr #\z))
          (+ (- (char-code chr) (char-code #\a)) 10))))

(defun value-digit (n)
   (if (< n 10)
       (code-char (+ n (char-code #\0)))
       (code-char (+ (- n 10) (char-code #\A)))))

(defun num-from-cs (cs base)
   (if (endp cs)
       0
       (+ (digit-value (first cs))
          (* base (num-from-cs (rest cs) base)))))

(defun parse-num (str base)
   (num-from-cs (reverse (coerce str 'list)) base))

(include-book "arithmetic-3/top" :dir :system)

(defun num-to-cs (num base)
   (if (or (zp num) (zp base) (= base 1))
       nil
       (cons (value-digit (mod num base))
             (num-to-cs (floor num base) base))))

(defun show-num (num base)
   (coerce (reverse (num-to-cs num base)) 'string))

Action!

CHAR ARRAY digits="0123456789abcdefghijklmnopqrstuvwxyz"

PROC CheckBase(BYTE b)
  IF b<2 OR b>digits(0) THEN
    PrintE("Base is out of range!")
    Break()
  FI
RETURN

PROC Encode(CARD v BYTE b CHAR ARRAY s)
  CARD d
  BYTE i,len
  CHAR tmp

  CheckBase(b)
  len=0
  DO
    d=v MOD b
    len==+1
    s(len)=digits(d+1)
    v==/b
  UNTIL v=0
  OD
  s(0)=len

  FOR i=1 to len/2
  DO
    tmp=s(i)
    s(i)=s(len-i+1)
    s(len-i+1)=tmp
  OD
RETURN

CARD FUNC Decode(CHAR ARRAY s BYTE b)
  CARD res
  BYTE i,j,found

  CheckBase(b)
  res=0
  FOR i=1 TO s(0)
  DO
    found=0
    FOR j=1 TO digits(0)
    DO
      IF digits(j)=s(i) THEN
        found=1 EXIT
      FI
    OD
    IF found=0 THEN
      PrintE("Unrecognized character!")
      Break()
    FI
    res==*b
    res==+j-1
  OD
RETURN (res)

PROC Main()
  CARD v=[6502],v2
  BYTE b
  CHAR ARRAY s(256)

  FOR b=2 TO 23
  DO
    Encode(v,b,s)
    v2=Decode(s,b)
    PrintF("%U -> base %B %S -> %U%E",v,b,s,v2)
  OD
RETURN
Output:

Screenshot from Atari 8-bit computer

6502 -> base 2 1100101100110 -> 6502
6502 -> base 3 22220211 -> 6502
6502 -> base 4 1211212 -> 6502
6502 -> base 5 202002 -> 6502
6502 -> base 6 50034 -> 6502
6502 -> base 7 24646 -> 6502
6502 -> base 8 14546 -> 6502
6502 -> base 9 8824 -> 6502
6502 -> base 10 6502 -> 6502
6502 -> base 11 4981 -> 6502
6502 -> base 12 391a -> 6502
6502 -> base 13 2c62 -> 6502
6502 -> base 14 2526 -> 6502
6502 -> base 15 1dd7 -> 6502
6502 -> base 16 1966 -> 6502
6502 -> base 17 1588 -> 6502
6502 -> base 18 1214 -> 6502
6502 -> base 19 i04 -> 6502
6502 -> base 20 g52 -> 6502
6502 -> base 21 efd -> 6502
6502 -> base 22 d9c -> 6502
6502 -> base 23 c6g -> 6502

Ada

Ada provides built-in capability to convert between all bases from 2 through 16. This task requires conversion for bases up to 36. The following program demonstrates such a conversion using an iterative solution.

with Ada.Text_Io; use Ada.Text_Io;
with Ada.Strings.Fixed;
With Ada.Strings.Unbounded;

procedure Number_Base_Conversion is
   Max_Base : constant := 36;
   subtype Base_Type is Integer range 2..Max_Base;
   Num_Digits : constant String := "0123456789abcdefghijklmnopqrstuvwxyz";
   Invalid_Digit : exception;
   
   function To_Decimal(Value : String; Base : Base_Type) return Integer is
      use Ada.Strings.Fixed;
      Result : Integer := 0;
      Decimal_Value : Integer;
      Radix_Offset : Natural := 0;
   begin
      for I in reverse Value'range loop
         Decimal_Value := Index(Num_Digits, Value(I..I)) - 1;
         if Decimal_Value < 0 then
            raise Invalid_Digit;
         end if; 
         Result := Result + (Base**Radix_Offset * Decimal_Value);
         Radix_Offset := Radix_Offset + 1;
      end loop;
      return Result;
   end To_Decimal;
   
   function To_Base(Value : Natural; Base : Base_Type) return String is
      use Ada.Strings.Unbounded;
      Result : Unbounded_String := Null_Unbounded_String;
      Temp : Natural := Value;
      Base_Digit : String(1..1);
   begin
      if Temp = 0 then
         return "0";
      end if;
      while Temp > 0 loop
         Base_Digit(1) := Num_Digits((Temp mod Base) + 1);
         if Result = Null_Unbounded_String then
            Append(Result, Base_Digit);
         else
            Insert(Source => Result,
               Before => 1,
               New_Item => Base_Digit);
         end if;
         Temp := Temp / Base;
      end loop;
      return To_String(Result);
   end To_Base;
   
begin
   Put_Line("26 converted to base 16 is " & To_Base(26, 16));
   Put_line("1a (base 16) is decimal" & Integer'image(To_Decimal("1a", 16)));
end Number_Base_Conversion;

Aime

o_text(bfxa(0, 0, 16, 1000000));
o_byte('\n');
o_text(bfxa(0, 0, 5, 1000000));
o_byte('\n');
o_text(bfxa(0, 0, 2, 1000000));
o_byte('\n');

o_integer(alpha("f4240", 16));
o_byte('\n');
o_integer(alpha("224000000", 5));
o_byte('\n');
o_integer(alpha("11110100001001000000", 2));
o_byte('\n');

ALGOL 68

Built in or standard distribution routines

Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

The formatted transput in ALGOL 68 uses the format type (mode). This format type has many similarities with modern regular expressions and can be used to convert string patterns to and from many of the built in types (modes) in ALGOL 68. Here is an example converting a numbers base.

INT base = 16, from dec = 26;
BITS to bits;

FORMAT hex repr = $n(base)r2d$;

FILE f; STRING str; 

associate(f, str);
putf(f, (hex repr, BIN from dec));
print(("Hex: ",str, new line));

reset(f);
getf(f, (hex repr, to bits));
print(("Int: ",ABS to bits, new line))

Output:

Hex: 1a
Int:         +26

Note that the only conversions "officially" available are for the bases 2r, 4r, 8r and 16r. But ALGOL 68G allows formatting for all numbers in the range 2r to 16r.

Implementation example

Handles signed and unsigned numbers from all bases.

Translation of: python
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386
STRING numeric alpha = "0123456789abcdefghijklmnopqrstuvwxyz";

PROC raise value error = ([]STRING args)VOID: (
  put(stand error, "Value error");
  STRING sep := ": ";
  FOR index TO UPB args - 1 DO put(stand error, (sep, args[index])); sep:=", " OD;
  new line(stand error);
  stop
);

PROC base n = (INT num, base)STRING: (
  PROC base n = (INT num, base)STRING:
    ( num = 0 | "" |  base n(num OVER base, base) + numeric alpha[@0][num MOD base]);
  ( num = 0 | "0" |: num > 0 | base n(num, base) | "-" + base n(-num, base) )
);

PROC unsigned int = (STRING repr, INT base)INT:
  IF UPB repr < LWB repr THEN 0 ELSE
    INT pos; 
    IF NOT char in string(repr[UPB repr], pos, numeric alpha) THEN 
      raise value error("CHAR """+repr[UPB repr]+""" not valid") 
    FI;
    unsigned int(repr[:UPB repr-1], base) * base + pos - 1
  FI
;

PROC int = (STRING repr, INT base)INT: 
  ( repr[LWB repr]="-" | -unsigned int(repr[LWB repr + 1:], base) | unsigned int(repr, base) );

[]INT test = (-256, -255, -26, -25, 0, 25, 26, 255, 256);
FOR index TO UPB test DO
  INT k = test[index];
  STRING s = base n(k,16); # returns the string 1a #
  INT i = int(s,16);  # returns the integer 26 #
  print((k," => ", s, " => ", i, new line))
OD

Output:

       -256 => -100 =>        -256
       -255 => -ff =>        -255
        -26 => -1a =>         -26
        -25 => -19 =>         -25
         +0 => 0 =>          +0
        +25 => 19 =>         +25
        +26 => 1a =>         +26
       +255 => ff =>        +255
       +256 => 100 =>        +256

Other libraries or implementation specific extensions

As of February 2009 no open source libraries to do this task have been located.

ALGOL W

begin
    % returns with numberInBase set to the number n converted to a string in %
    % the specified base. Number must be non-negative and base must be in    %
    % range 2 to 36                                                          %
    procedure convertToBase( integer    value  n
                           ; integer    value  base
                           ; string(32) result numberInBase
                           ) ;
    begin
        string(36) baseDigits;
        integer    val, strPos;

        assert( n >= 0 and base >= 2 and base <= 36 );

        baseDigits    := "0123456789abcdefghijklmnopqrstuvwxyz";
        numberInBase  := " ";
        val           := n;
        strPos        := 31;
        while
            begin
                % a(b//c) is the substring of a starting at b with length c. %
                % The first character is at position 0. The length must be   %
                % an integer literal so it is known at compile time.         %
                numberInBase( strPos // 1 ) := baseDigits( val rem base // 1 );
                val    := val div base;
                strPos := strPos - 1;
                val > 0
            end
        do begin end
    end convertToBase ;

    % returns the string numberInBase converted to an integer assuming       %
    % numberInBase ia a string in the specified base                         %
    % base must be in range 2 to 36, invalid digits will cause the program   %
    % to crash, spaces are ignored                                           %
    integer procedure convertFromBase( string(32) value numberInBase
                                     ; integer    value base
                                     ) ;
    begin
        string(36) baseDigits;
        integer    val, cPos;

        assert( base >= 2 and base <= 36 );

        baseDigits    := "0123456789abcdefghijklmnopqrstuvwxyz";
        val           := 0;
        for strPos := 0 until 31 do begin
            string(1) c;
            c := numberInBase( strPos // 1 );
            if c not = " " then begin
                cPos := 0;
                while baseDigits( cPos // 1 ) not = c do cPos := cPos + 1;
                val  := ( val * base ) + cPos;
            end
        end;
        val
    end convertFromBase ;

    % test the procedures                                                    %
    string(32) baseNumber;
    i_w := 3; % set integer output width                                     %
    for i := 2 until 36 do begin
        convertToBase( 35, i, baseNumber );
        write( 35, i, baseNumber, " ", convertFromBase( baseNumber, i ) );
    end
end.

AppleScript

Translation of: JavaScript

For more flexibility with digit variants (upper and lower case hex, digits in other languages/scripts etc) we can define toBase(intBase, n) in terms of a more general inBaseDigits(strDigits, n) which derives the base from the number of digits to be used:

-- toBase :: Int -> Int -> String
on toBase(intBase, n)
    if (intBase < 36) and (intBase > 0) then
        inBaseDigits(items 1 thru intBase of "0123456789abcdefghijklmnopqrstuvwxyz", n)
    else
        "not defined for base " & (n as string)
    end if
end toBase

-- inBaseDigits :: String -> Int -> [String]
on inBaseDigits(strDigits, n)
    set intBase to length of strDigits
    
    script nextDigit
        on |λ|(residue)
            set {divided, remainder} to quotRem(residue, intBase)
            if divided > 0 then
                {just:(item (remainder + 1) of strDigits), new:divided, nothing:false}
            else
                {nothing:true}
            end if
            
        end |λ|
    end script
    
    reverse of unfoldr(nextDigit, n) as string
end inBaseDigits

-- OTHER FUNCTIONS DERIVABLE FROM inBaseDigits -------------------------------

-- inUpperHex :: Int -> String
on inUpperHex(n)
    inBaseDigits("0123456789ABCDEF", n)
end inUpperHex

-- inDevanagariDecimal :: Int -> String
on inDevanagariDecimal(n)
    inBaseDigits("०१२३४५६७८९", n)
end inDevanagariDecimal

-- TEST ----------------------------------------------------------------------
on run
    script
        on |λ|(x)
            {{binary:toBase(2, x), octal:toBase(8, x), hex:toBase(16, x)}, ¬
                {upperHex:inUpperHex(x), dgDecimal:inDevanagariDecimal(x)}}
        end |λ|
    end script
    
    map(result, [255, 240])
end run


-- GENERIC FUNCTIONS ---------------------------------------------------------

-- unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
on unfoldr(f, v)
    set lst to {}
    set recM to {nothing:false, new:v}
    tell mReturn(f)
        repeat while (not (nothing of recM))
            set recM to |λ|(new of recM)
            if not nothing of recM then set end of lst to just of recM
        end repeat
    end tell
    lst
end unfoldr

--  quotRem :: Integral a => a -> a -> (a, a)
on quotRem(m, n)
    {m div n, m mod n}
end quotRem

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn
Output:
{{{binary:"11111111", octal:"377", hex:"ff"}, {upperHex:"FF", dgDecimal:"२५५"}}, 
{{binary:"11110000", octal:"360", hex:"f0"}, {upperHex:"F0", dgDecimal:"२४०"}}}

Arturo

fromBase: function [x,base][
    if base=2 [ return from.binary x ]
    if base=8 [ return from.octal x ]
    if base=16 [ return from.hex x ]

    return to :integer x
]

toBase: function [x,base][
    if base=2 [ return as.binary x ]
    if base=8 [ return as.octal x ]
    if base=16 [ return as.hex x ]

    return to :string x
]

loop 1..20 'i ->
    print [
        i "base2:" toBase i 2 "base8:" toBase i 8 "base16:" toBase i 16
    ]

print ""

print ["101 => from base2:" fromBase "101" 2 "from base8:" fromBase "101" 8 "from base16:" fromBase "101" 16]
print ["123 => from base8:" fromBase "123" 8 "from base16:" fromBase "123" 16]
print ["456 => from base8:" fromBase "456" 8 "from base16:" fromBase "456" 16]
Output:
1 base2: 1 base8: 1 base16: 1 
2 base2: 10 base8: 2 base16: 2 
3 base2: 11 base8: 3 base16: 3 
4 base2: 100 base8: 4 base16: 4 
5 base2: 101 base8: 5 base16: 5 
6 base2: 110 base8: 6 base16: 6 
7 base2: 111 base8: 7 base16: 7 
8 base2: 1000 base8: 10 base16: 8 
9 base2: 1001 base8: 11 base16: 9 
10 base2: 1010 base8: 12 base16: a 
11 base2: 1011 base8: 13 base16: b 
12 base2: 1100 base8: 14 base16: c 
13 base2: 1101 base8: 15 base16: d 
14 base2: 1110 base8: 16 base16: e 
15 base2: 1111 base8: 17 base16: f 
16 base2: 10000 base8: 20 base16: 10 
17 base2: 10001 base8: 21 base16: 11 
18 base2: 10010 base8: 22 base16: 12 
19 base2: 10011 base8: 23 base16: 13 
20 base2: 10100 base8: 24 base16: 14 

101 => from base2: 5 from base8: 65 from base16: 257 
123 => from base8: 83 from base16: 291 
456 => from base8: 302 from base16: 1110

AutoHotkey

MsgBox % number2base(200, 16) ; 12
MsgBox % parse(200, 16)  ; 512

number2base(number, base)
{
  While, base < digit := floor(number / base)
  {
    result := mod(number, base) . result
    number := digit
  }
  result := digit . result
  Return result
}

parse(number, base)
{
  result = 0
  pos := StrLen(number) - 1
  Loop, Parse, number 
  {
    result := ((base ** pos) * A_LoopField) + result
    base -= 1
  }
  Return result
}

alternate implementation contributed by Laszlo on the ahk forum

MsgBox % ToBase(29,3)
MsgBox % ToBase(255,16)

MsgBox % FromBase("100",8)
MsgBox % FromBase("ff",16)

ToBase(n,b) { ; n >= 0, 1 < b <= 36
   Return (n < b ? "" : ToBase(n//b,b)) . ((d:=mod(n,b)) < 10 ? d : Chr(d+87))
}

FromBase(s,b) { ; convert base b number s=strings of 0..9,a..z, to AHK number
   Return (L:=StrLen(s))=0 ? "":(L>1 ? FromBase(SubStr(s,1,L-1),b)*b:0) + ((c:=Asc(SubStr(s,0)))>57 ? c-87:c-48)
}

AWK

function strtol(str, base)
{
  symbols = "0123456789abcdefghijklmnopqrstuvwxyz"
  res = 0
  str = tolower(str)
  for(i=1; i < length(str); i++) {
    res += index(symbols, substr(str, i, 1)) - 1
    res *= base
  }
  res += index(symbols, substr(str, length(str), 1)) - 1
  return res
}

function ltostr(num, base)
{
  symbols = "0123456789abcdefghijklmnopqrstuvwxyz"
  res = ""
  do {
    res = substr(symbols, num%base + 1, 1) res
    num = int(num/base)
  } while ( num != 0 )
  return res
}

BEGIN {
  print strtol("7b", 16)
  print ltostr(123, 16)
}

BBC BASIC

      PRINT "  0 (decimal) -> " FNtobase(0, 16) " (base 16)"
      PRINT " 26 (decimal) -> " FNtobase(26, 16) " (base 16)"
      PRINT "383 (decimal) -> " FNtobase(383, 16) " (base 16)"
      PRINT " 26 (decimal) -> " FNtobase(26, 2) " (base 2)"
      PRINT "383 (decimal) -> " FNtobase(383, 2) " (base 2)"
      PRINT " 1a (base 16) -> " ;FNfrombase("1a", 16) " (decimal)"
      PRINT " 1A (base 16) -> " ;FNfrombase("1A", 16) " (decimal)"
      PRINT "17f (base 16) -> " ;FNfrombase("17f", 16) " (decimal)"
      PRINT "101111111 (base 2) -> " ;FNfrombase("101111111", 2) " (decimal)"
      END
      
      DEF FNtobase(N%, B%)
      LOCAL D%,A$
      REPEAT
        D% = N% MOD B%
        N% DIV= B%
        A$ = CHR$(48 + D% - 39*(D%>9)) + A$
      UNTIL N% = FALSE
      =A$
      
      DEF FNfrombase(A$, B%)
      LOCAL N%
      REPEAT
        N% *= B%
        N% += ASC(A$) - 48 + 7*(ASCA$>64) + 32*(ASCA$>96)
        A$ = MID$(A$,2)
      UNTIL A$ = ""
      = N%

Output:

  0 (decimal) -> 0 (base 16)
 26 (decimal) -> 1a (base 16)
383 (decimal) -> 17f (base 16)
 26 (decimal) -> 11010 (base 2)
383 (decimal) -> 101111111 (base 2)
 1a (base 16) -> 26 (decimal)
 1A (base 16) -> 26 (decimal)
17f (base 16) -> 383 (decimal)
101111111 (base 2) -> 383 (decimal)

BCPL

get "libhdr";

// Reverse a string
let reverse(str) = valof
$(  let i = 1
    let j = str%0
    while i<j
    $(  let c = str%i
        str%i := str%j
        str%j := c
        i := i+1
        j := j-1
    $)
    resultis str
$)

// Convert number to string given base
let itoa(n, base, buf) = valof
$(  let digitchar(n) = 
        n < 10 -> n + '0',
        (n - 10) + 'A'
    buf%0 := 0
    $( buf%0 := buf%0 + 1
       buf%(buf%0) := digitchar(n rem base)
       n := n / base
    $) repeatuntil n<=0
    resultis reverse(buf)
$)

// Convert string to number given base
let atoi(str, base) = valof
$(  let digitval(d, base) = 
        '0' <= d <= '9' -> d - '0',
        'A' <= d <= 'Z' -> (d - 'A') + 10,
        'a' <= d <= 'z' -> (d - 'a') + 10,
        0
    let result = 0
    for i=1 to str%0 do
        result := result * base + digitval(str%i, base)
    resultis result
$)

// Examples
let start() be
$(  let buffer = vec 64

    writes("1234 in bases 2-36:*N")
    for base=2 to 36 do
        writef("Base %I2: %S*N", base, itoa(1234, base, buffer))
        
    writes("*N*"25*" in bases 10-36:*N")
    for base=10 to 36 do
        writef("Base %I2: %N*N", base, atoi("25", base))
$)
Output:
1234 in bases 2-36:
Base  2: 10011010010
Base  3: 1200201
Base  4: 103102
Base  5: 14414
Base  6: 5414
Base  7: 3412
Base  8: 2322
Base  9: 1621
Base 10: 1234
Base 11: A22
Base 12: 86A
Base 13: 73C
Base 14: 642
Base 15: 574
Base 16: 4D2
Base 17: 44A
Base 18: 3EA
Base 19: 37I
Base 20: 31E
Base 21: 2GG
Base 22: 2C2
Base 23: 27F
Base 24: 23A
Base 25: 1O9
Base 26: 1LC
Base 27: 1IJ
Base 28: 1G2
Base 29: 1DG
Base 30: 1B4
Base 31: 18P
Base 32: 16I
Base 33: 14D
Base 34: 12A
Base 35: 109
Base 36: YA

"25" in bases 10-36:
Base 10: 25
Base 11: 27
Base 12: 29
Base 13: 31
Base 14: 33
Base 15: 35
Base 16: 37
Base 17: 39
Base 18: 41
Base 19: 43
Base 20: 45
Base 21: 47
Base 22: 49
Base 23: 51
Base 24: 53
Base 25: 55
Base 26: 57
Base 27: 59
Base 28: 61
Base 29: 63
Base 30: 65
Base 31: 67
Base 32: 69
Base 33: 71
Base 34: 73
Base 35: 75
Base 36: 77

Bracmat

  ( display
  =   
    .   !arg:<10
      | !arg:<36&chr$(asc$a+!arg+-10)
      | "Base too big"
  )
& ( base
  =   n b
    .     !arg:(?n.?b)
        & !n:<!b
        & ( !n:~<0&display$!n
          | NOTSUPPORTED
          )
      | base$(div$(!n.!b).!b) display$(mod$(!n.!b))
  )
&   whl
  ' (   put
      $ "Enter non-negative integer in decimal notation (or something else to stop):"
    & get':~/#>-1:?n
    & put$"Enter base (less than 37):"
    & get$:~/#>1:~>36:?b
    & out$(!n " in base " !b " is " str$(base$(!n.!b)))
    );

C

#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <stdint.h>

char *to_base(int64_t num, int base)
{
  char *tbl = "0123456789abcdefghijklmnopqrstuvwxyz";
  char buf[66] = {'\0'};
  char *out;
  uint64_t n;
  int i, len = 0, neg = 0;
  if (base > 36) {
    fprintf(stderr, "base %d too large\n", base);
    return 0;
  }

  /* safe against most negative integer */ 
  n = ((neg = num < 0)) ? (~num) + 1 : num;

  do { buf[len++] = tbl[n % base]; } while(n /= base);

  out = malloc(len + neg + 1);
  for (i = neg; len > 0; i++) out[i] = buf[--len];
  if (neg) out[0] = '-';

  return out;
}

long from_base(const char *num_str, int base)
{
  char *endptr;
  /* there is also strtoul() for parsing into an unsigned long */
  /* in C99, there is also strtoll() and strtoull() for parsing into long long and
   * unsigned long long, respectively */
  int result = strtol(num_str, &endptr, base);
  return result;
}

int main()
{
  int64_t x;
  x = ~(1LL << 63) + 1;
  printf("%lld in base 2: %s\n", x, to_base(x, 2));
  x = 383;
  printf("%lld in base 16: %s\n", x, to_base(x, 16));
  return 0;
}
output
-9223372036854775808 in base 2: -1000000000000000000000000000000000000000000000000000000000000000
383 in base 16: 17f

C#

public static class BaseConverter {

    /// <summary>
    /// Converts a string to a number
    /// </summary>
    /// <returns>The number.</returns>
    /// <param name="s">The string to convert.</param>
    /// <param name="b">The base number (between 2 and 36).</param>
    public static long stringToLong(string s, int b) {

        if ( b < 2 || b > 36 )
            throw new ArgumentException("Base must be between 2 and 36", "b");

        checked {

            int slen = s.Length;
            long result = 0;
            bool isNegative = false;

            for ( int i = 0; i < slen; i++ ) {

                char c = s[i];
                int num;

                if ( c == '-' ) {
                    // Negative sign
                    if ( i != 0 )
                        throw new ArgumentException("A negative sign is allowed only as the first character of the string.", "s");

                    isNegative = true;
                    continue;
                }

                if ( c > 0x2F && c < 0x3A )
                    // Numeric character (subtract from 0x30 ('0') to get numerical value)
                    num = c - 0x30;
                else if ( c > 0x40 && c < 0x5B )
                    // Uppercase letter
                    // Subtract from 0x41 ('A'), then add 10
                    num = c - 0x37;  // 0x37 = 0x41 - 10
                else if ( c > 0x60 && c < 0x7B )
                    // Lowercase letter
                    // Subtract from 0x61 ('a'), then add 10
                    num = c - 0x57;  // 0x57 = 0x61 - 10
                else
                    throw new ArgumentException("The string contains an invalid character '" + c + "'", "s");

                // Check that the digit is allowed by the base.

                if ( num >= b )
                    throw new ArgumentException("The string contains a character '" + c + "' which is not allowed in base " + b, "s");

                // Multiply the result by the base, then add the next digit

                result *= b;
                result += num;

            }

            if ( isNegative )
                result = -result;

            return result;

        }

    }

    /// <summary>
    /// Converts a number to a string.
    /// </summary>
    /// <returns>The string.</returns>
    /// <param name="n">The number to convert.</param>
    /// <param name="b">The base number (between 2 and 36).</param>
    public static string longToString(long n, int b) {
        
        // This uses StringBuilder, so it only works with .NET 4.0 or higher. For earlier versions, the StringBuilder
        // can be replaced with simple string concatenation.
        
        if ( b < 2 || b > 36 )
            throw new ArgumentException("Base must be between 2 and 36", "b");

        // If the base is 10, call ToString() directly, which returns a base-10 string.

        if ( b == 10 )
            return n.ToString();

        checked {
            long longBase = b;
            
            StringBuilder sb = new StringBuilder();
            
            if ( n < 0 ) {
                // Negative numbers
                n = -n;
                sb.Append('-');
            }
            
            long div = 1;
            while ( n / div >= b )
                // Continue multiplying the dividend by the base until it reaches the greatest power of
                // the base which is less than or equal to the number.
                div *= b;
            
            while ( true ) {
                byte digit = (byte) (n / div);
            
                if ( digit < 10 )
                    // Numeric character (0x30 = '0')
                    sb.Append((char) (digit + 0x30));
                else
                    // Alphabetic character (for digits > 10) (0x61 = 'a')
                    sb.Append((char) (digit + 0x57));  // 0x61 - 10
            
                if ( div == 1 )
                    // Stop when the dividend reaches 1
                    break;
            
                n %= div;
                div /= b;
            }
            
            return sb.ToString();
        }

    }

}

C++

#include <string>
#include <cstdlib>
#include <algorithm>
#include <cassert>

std::string const digits = "0123456789abcdefghijklmnopqrstuvwxyz";

std::string to_base(unsigned long num, int base)
{
  if (num == 0)
    return "0";
  
  std::string result;
  while (num > 0) {
    std::ldiv_t temp = std::div(num, (long)base);
    result += digits[temp.rem];
    num = temp.quot;
  }
  std::reverse(result.begin(), result.end());
  return result;
}

unsigned long from_base(std::string const& num_str, int base)
{
  unsigned long result = 0;
  for (std::string::size_type pos = 0; pos < num_str.length(); ++pos)
    result = result * base + digits.find(num_str[pos]);
  return result;
}

Caché ObjectScript

Class Utils.Number [ Abstract ]
{

ClassMethod ConvertBase10ToN(pNum As %Integer = "", pBase As %Integer = "", pBaseStr As %String = "", pPos As %Integer = 0) As %String
{
  If pNum=0 Quit ""
  Set str=..ConvertBase10ToN(pNum\pBase, pBase, pBaseStr, pPos+1)
  Quit str_$Extract(pBaseStr, pNum#pBase+1)
}

ClassMethod ConvertBaseNTo10(pStr As %String = "", pBase As %Integer = "", pBaseStr As %String = "", pPos As %Integer = 0) As %Integer
{
  If pStr="" Quit 0
  Set num=..ConvertBaseNTo10($Extract(pStr, 1, *-1), pBase, pBaseStr, pPos+1)
  Set dec=$Find(pBaseStr, $Extract(pStr, *))-2
  Quit num+(dec*(pBase**pPos))
}

ClassMethod ConvertBase(pStr As %String = "", pFrom As %Integer = 10, pTo As %Integer = 10, pBaseStr As %String = "", pLen As %Integer = 0) As %String
{
  // some initialisation
  If pBaseStr="" Set pBaseStr="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
  
  // check input values
  If pFrom=10 Set pStr=$Number(pStr, "i", 0) If pStr="" Quit ""
  Set pFrom=$Number(pFrom, "i", 2, 94) If pFrom="" Quit ""
  Set pTo=$Number(pTo, "i", 2, 94) If pTo="" Quit ""
  Set pLen=$Number(pLen, "i", 0, 32) If pLen="" Quit ""
  
  // does base number exceed base string?
  If pFrom>$Length(pBaseStr) Quit ""
  If pTo>$Length(pBaseStr) Quit ""
  
  // allow for upper/lowercase values
  If pTo=10 {
    If $Match(pStr, "^[0-9a-z]+$"), $Match($Extract(pBaseStr, 1, pFrom), "^[0-9A-Z]+$") {
      Set pStr=$ZConvert(pStr, "U")
    }
    If $Match(pStr, "^[0-9A-Z]+$"), $Match($Extract(pBaseStr, 1, pFrom), "^[0-9a-z]+$") {
      Set pStr=$ZConvert(pStr, "L")
    }
  }
  
  // do the conversion
  If pFrom=pTo {
    Set pStr=pStr
  } ElseIf pFrom=10 {
    Set pStr=..ConvertBase10ToN($Select(pStr=0: "", 1: pStr), pTo, pBaseStr)
  } ElseIf pTo=10 {
    Set pStr=..ConvertBaseNTo10(pStr, pFrom, pBaseStr)
  } Else {
    Set pStr=..ConvertBase10ToN(..ConvertBaseNTo10(pStr, pFrom, pBaseStr), pTo, pBaseStr)
  }
  
  // return value
  If pLen=0 Quit pStr
  If pTo'=10 Quit ..PadStr(pStr, pLen, $Extract(pBaseStr))
  Quit ..PadStr(pStr, pLen)
}

ClassMethod PadStr(pStr As %String, pLen As %Integer, pZero As %String = 0) As %String [ Private ]
{
  If $Length(pStr)>pLen Quit pStr
  Quit $Translate($Justify(pStr, pLen), " ", pZero)
}

}
Examples:
USER>Write ##class(Utils.Number).ConvertBase(1010101111001101, 2, 16)
ABCD

USER>Write $ZHex(26)
1A
USER>Write $ZHex("1A")
26

USER>Write ##class(Utils.Number).ConvertBase(26, 10, 16)
1A
USER>Write ##class(Utils.Number).ConvertBase("1A", 16, 10)
26

USER>Write ##class(Utils.Number).ConvertBase(6234900123456700, 10, 42, "!$%-0123456789@ABCDEFGHIJKLMNOPQRSTUVWXYZ_")
A9XUCDBHK6
USER>Write ##class(Utils.Number).ConvertBase("A9XUCDBHK6", 42, 10, "!$%-0123456789@ABCDEFGHIJKLMNOPQRSTUVWXYZ_")
6234900123456700

Common Lisp

(parse-integer "1a" :radix 16) ; returns multiple values: 26, 2
(write-to-string 26 :base 16) ; also "1A"

Alternative implementation using FORMAT's ~R directive and #nR reader macro

(defun decimal-to-base-n (number &key (base 16))
  (format nil (format nil "~~~dr" base) number))

(defun base-n-to-decimal (number &key (base 16))
  (read-from-string (format nil "#~dr~d" base number)))

Yet another approach uses FORMAT's ~R in conjunction with ~V for passing arguments to directives (this assumes input as string)

(defun change-base (number input-base output-base)
  (format nil "~vr" output-base (parse-integer number :radix input-base)))

D

Using Standard Functions

import std.stdio, std.conv, std.string, std.ascii;

void main() {
    "1abcd".to!int(16).writeln;

    writeln(60_272_032_366.to!string(36, LetterCase.lower), ' ',
            591_458.to!string(36, LetterCase.lower));
}
Output:
109517
rosetta code

One Implementation

import std.stdio, std.array, std.ascii;

immutable string mDigits = digits ~ lowercase;

ulong atoiRadix(in string str, in uint radix=10, int* consumed=null)
nothrow {
    static int dtoi(in char dc, in uint radix) nothrow {
        static int[immutable char] digit;
        immutable char d = dc.toLower;
        if (digit.length == 0) // Not init yet.
            foreach (i, c; mDigits)
                digit[c] = i;
        if (radix > 1 && radix <= digit.length &&
            d in digit && digit[d] < radix)
            return digit[d];
        return int.min; // A negative for error.
    }

    ulong result;
    int sp;
    for (; sp < str.length; sp++) {
        immutable int d = dtoi(str[sp], radix);
        if (d >= 0) // Valid digit char.
            result = radix * result + d;
        else
            break;
    }
    if (sp != str.length) // Some char in str not converted.
        sp = -sp;
    if (consumed !is null) // Signal error if not positive.
        *consumed = sp;
    return result;
}

string itoaRadix(ulong num, in uint radix=10) pure nothrow
in {
    assert(radix > 1 && radix <= mDigits.length);
} body {
    string result;
    while (num > 0) {
        immutable uint d = num % radix;
        result = mDigits[d] ~ result;
        num = (num - d) / radix;
    }
    return result.empty ? "0" : result;
}

void main() {
    immutable string numStr = "1ABcdxyz???";

    int ate;
    writef("'%s' (base %d) = %d", numStr, 16,
           atoiRadix(numStr, 16, &ate));

    if (ate <= 0)
        writefln("\tConverted only: '%s'", numStr[0 .. -ate]);
    else
        writeln();

    writeln(itoaRadix(60_272_032_366, 36), " ",
            itoaRadix(591_458, 36));
}
Output:
'1ABcdxyz???' (base 16) = 109517    Converted only: '1ABcd'
rosetta code

Alternative Implementation

Translation of: Haskell
import std.stdio, std.algorithm, std.ascii, std.array, std.string;

alias Digits = ubyte[];

Digits toBase(ulong number, in ubyte base) pure nothrow @safe {
    Digits result;
    while (number) {
        result = number % base ~ result;
        number /= base;
    }
    return result;
}

enum fromBase = (in Digits digits, in ubyte base) pure nothrow @safe @nogc =>
    reduce!((n, k) => n * base + k)(0UL, digits);

immutable myDigits = digits ~ lowercase;

enum fromDigits = (in Digits digits) pure nothrow /*@safe*/ =>
    digits.map!(d => myDigits[d]).array;

enum convert = (in dchar d) pure nothrow @safe @nogc =>
    cast(ubyte)(d.isDigit ? d - '0' : std.ascii.toLower(d) - 'a' + 10);

enum toDigits = (in string number) pure nothrow @safe =>
    number.representation.map!convert.array;

void main() {
    "1ABcd".toDigits.fromBase(16).writeln;
}
Output:
109517

Delphi

Works with: Delphi version 6.0


function GetRadixString(L: Integer; Radix: Byte): string;
{Converts integer a string of any radix}
const RadixChars: array[0..35] Of char =
    ('0', '1', '2', '3', '4', '5', '6', '7',
     '8', '9', 'A', 'B', 'C', 'D', 'E', 'F',
     'G','H', 'I', 'J', 'K', 'L', 'M', 'N',
     'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V',
     'W', 'X', 'Y', 'Z');
var I: integer;
var S: string;
var Sign: string[1];
begin
Result:='';
If (L < 0) then
	begin
	Sign:='-';
	L:=Abs(L);
	end
else Sign:='';
S:='';
repeat
	begin
	I:=L mod Radix;
	S:=RadixChars[I] + S;
	L:=L div Radix;
	end
until L = 0;
Result:=Sign + S;
end;

procedure ShowRadixConvertion(Memo: TMemo);
var B,N: integer;
var S,RS: string;
begin
N:=6502;
for B:=2 to 23 do
	begin
	RS:=GetRadixString(N,B);
	RS:=LowerCase(RS);
	Memo.Lines.Add(Format('%5d -> base: %3D = %15S',[N,B,RS]));
	end;
end;
Output:
 6502 -> base:   2 =   1100101100110
 6502 -> base:   3 =        22220211
 6502 -> base:   4 =         1211212
 6502 -> base:   5 =          202002
 6502 -> base:   6 =           50034
 6502 -> base:   7 =           24646
 6502 -> base:   8 =           14546
 6502 -> base:   9 =            8824
 6502 -> base:  10 =            6502
 6502 -> base:  11 =            4981
 6502 -> base:  12 =            391a
 6502 -> base:  13 =            2c62
 6502 -> base:  14 =            2526
 6502 -> base:  15 =            1dd7
 6502 -> base:  16 =            1966
 6502 -> base:  17 =            1588
 6502 -> base:  18 =            1214
 6502 -> base:  19 =             i04
 6502 -> base:  20 =             g52
 6502 -> base:  21 =             efd
 6502 -> base:  22 =             d9c
 6502 -> base:  23 =             c6g


E

def stringToInteger := __makeInt
def integerToString(i :int, base :int) {
  return i.toString(base)
}
? stringToInteger("200", 16)
# value: 512

? integerToString(200, 16)
# value: "c8"

EasyLang

func$ num2str n base .
   if n = 0
      return "0"
   .
   d = n mod base
   if d > 9
      d += 39
   .
   d$ = strchar (d + 48)
   if n < base
      return d$
   .
   return num2str (n div base) base & d$
.
func str2num s$ base .
   r = 0
   for c$ in strchars s$
      d = strcode c$ - 48
      if d > 9
         d -= 39
      .
      r = r * base + d
   .
   return r
.
print num2str 253 16
print str2num "fd" 16
print num2str 0 16

Elixir

iex(1)> String.to_integer("ffff", 16)
65535
iex(2)> Integer.to_string(255, 2)
"11111111"
iex(3)> String.to_integer("NonDecimalRadices", 36)
188498506820338115928429652

Erlang

Output:
12> erlang:list_to_integer("ffff", 17).
78300
13> erlang:integer_to_list(63, 3).
"2100"

Euphoria

function to_base(integer i, integer base)
    integer rem
    sequence s
    s = ""
    while i > 0 do
        rem = remainder(i,base)
        if rem < 10 then
            s = prepend(s, '0'+rem)
        else
            s = prepend(s, 'a'-10+rem)
        end if
        i = floor(i/base)
    end while
    
    if length(s) = 0 then
        s = "0"
    end if
    
    return s
end function

function from_base(sequence s, integer base)
    integer i,d
    i = 0
    for n = 1 to length(s) do
        i *= base
        if s[n] >= '0' and s[n] <= '9' then
            d = s[n]-'0'
        elsif s[n] >= 'a' then
            d = s[n]-'a'+10
        end if
        i += d
    end for
    return i
end function

Factor

USE: math.parser

12345 16 >base .
"3039" 16 base> .

Forth

Forth has a global user variable, BASE, which determines the radix used for parsing, interpretation, and printing of integers. This can handle bases from 2-36, but there are two words to switch to the most popular bases, DECIMAL and HEX.

42 dup
2 base !
.   \ 101010
hex
.   \ 2A
decimal

Many variants of Forth support literals in some bases, such as hex, using a prefix

$ff .   \ 255

Fortran

Works with: Fortran version 90 and later
MODULE Conversion
  IMPLICIT NONE
  CHARACTER(36) :: alphanum = "0123456789abcdefghijklmnopqrstuvwxyz"
 
  CONTAINS

  FUNCTION ToDecimal(base, instr)
    INTEGER :: ToDecimal
    INTEGER :: length, i, n, base
    CHARACTER(*) :: instr

    ToDecimal = 0
    length = LEN(instr)
    DO i = 1, length
      n = INDEX(alphanum, instr(i:i)) - 1
      n = n * base**(length-i)
      Todecimal = ToDecimal + n
    END DO
  END FUNCTION ToDecimal

  FUNCTION ToBase(base, number)
    CHARACTER(31) :: ToBase
    INTEGER :: base, number, i, rem

    ToBase = "                               "
    DO i = 31, 1, -1
      IF(number < base) THEN
        ToBase(i:i) = alphanum(number+1:number+1)
        EXIT
      END IF
      rem = MOD(number, base)
      ToBase(i:i) = alphanum(rem+1:rem+1)
      number = number / base
    END DO
    ToBase = ADJUSTL(ToBase)
  END FUNCTION ToBase

END MODULE Conversion

PROGRAM Base_Convert
  USE Conversion

  WRITE (*,*) ToDecimal(16, "1a")
  WRITE (*,*) ToBase(16, 26)     

END PROGRAM

FreeBASIC

' FB 1.05.0 Win64

Function min(x As Integer, y As Integer) As Integer
  Return IIf(x < y, x, y)
End Function

Function convertToBase (n As UInteger, b As UInteger) As String  
  If n < 2 OrElse b < 2 OrElse b = 10 OrElse b > 36 Then Return Str(n)
  Dim result As String = "" 
  Dim digit As Integer
  While n > 0
    digit = n Mod b
    If digit < 10 Then
      result = digit & result
    Else
      result = Chr(digit + 87) + result
    End If
     n \= b
  Wend
  Return result
End Function

Function convertToDecimal (s As Const String, b As UInteger) As UInteger
  If b < 2 OrElse b > 36 Then Return 0
  Dim t As String = LCase(s)
  Dim result As UInteger = 0
  Dim digit As Integer
  Dim multiplier As Integer = 1
  For i As Integer = Len(t) - 1 To 0 Step - 1
     digit = -1
     If t[i] >= 48 AndAlso t[i] <= min(57, 47 + b) Then
       digit = t[i] - 48
     ElseIf b > 10 AndAlso t[i] >= 97 AndAlso t[i] <= min(122, 87 + b) Then
       digit = t[i] - 87
     End If
     If digit = -1 Then Return 0 '' invalid digit present
     If digit > 0 Then result += multiplier * digit
     multiplier *= b
  Next
  Return result
End Function

Dim s As String

For b As UInteger = 2 To 36
  Print "36 base ";
  Print Using "##"; b; 
  s = ConvertToBase(36, b)
  Print " = "; s; Tab(21); " -> base ";
  Print Using "##"; b; 
  Print " = "; convertToDecimal(s, b)
Next

Print
Print "Press any key to quit"
Sleep
Output:
36 base  2 = 100100  -> base  2 = 36
36 base  3 = 1100    -> base  3 = 36
36 base  4 = 210     -> base  4 = 36
36 base  5 = 121     -> base  5 = 36
36 base  6 = 100     -> base  6 = 36
36 base  7 = 51      -> base  7 = 36
36 base  8 = 44      -> base  8 = 36
36 base  9 = 40      -> base  9 = 36
36 base 10 = 36      -> base 10 = 36
36 base 11 = 33      -> base 11 = 36
36 base 12 = 30      -> base 12 = 36
36 base 13 = 2a      -> base 13 = 36
36 base 14 = 28      -> base 14 = 36
36 base 15 = 26      -> base 15 = 36
36 base 16 = 24      -> base 16 = 36
36 base 17 = 22      -> base 17 = 36
36 base 18 = 20      -> base 18 = 36
36 base 19 = 1h      -> base 19 = 36
36 base 20 = 1g      -> base 20 = 36
36 base 21 = 1f      -> base 21 = 36
36 base 22 = 1e      -> base 22 = 36
36 base 23 = 1d      -> base 23 = 36
36 base 24 = 1c      -> base 24 = 36
36 base 25 = 1b      -> base 25 = 36
36 base 26 = 1a      -> base 26 = 36
36 base 27 = 19      -> base 27 = 36
36 base 28 = 18      -> base 28 = 36
36 base 29 = 17      -> base 29 = 36
36 base 30 = 16      -> base 30 = 36
36 base 31 = 15      -> base 31 = 36
36 base 32 = 14      -> base 32 = 36
36 base 33 = 13      -> base 33 = 36
36 base 34 = 12      -> base 34 = 36
36 base 35 = 11      -> base 35 = 36
36 base 36 = 10      -> base 36 = 36

FunL

Converting from integer to string:

$stdout = int( '1a', 16 )
Output:
26

Converting from string to integer:

$stdout = str( 26, 16 )
Output:
1a

Go

The standard strconv package functions ParseInt, ParseUint, FormatInt, FormatUint, and the standard math/big package method SetString, all accept a base argument 2 ≤ base ≤ 36.

Note, there is no equivalent formatting function provided for a big.Int, only the standard bases are available via fmt integer formatting verbs (binary %b, octal %o, decimal %d, and hexidecimal %x or %X).

package main

import (
    "fmt"
    "math/big"
    "strconv"
)

func main () {
    s := strconv.FormatInt(26, 16) // returns the string "1a"
    fmt.Println(s)

    i, err := strconv.ParseInt("1a", 16, 64) // returns the integer (int64) 26
    if err == nil {
        fmt.Println(i)
    }
    b, ok := new(big.Int).SetString("1a", 16) // returns the big integer 26
    if ok {
        fmt.Println(b)
    }
}

Groovy

Solution:

def radixParse = { s, radix -> Integer.parseInt(s, radix) }
def radixFormat = { i, radix -> Integer.toString(i, radix) }

Test Program:

def numString = '101'
(2..Character.MAX_RADIX).each { radix ->
    def value = radixParse(numString, radix)
    assert value == radix**2 + 1
    printf ("         %3s (%2d) == %4d (10)\n", numString, radix, value)
    
    def valM2str = radixFormat(value - 2, radix)
    def biggestDigit = radixFormat(radix - 1, radix)
    assert valM2str == biggestDigit + biggestDigit
    printf ("%3s (%2d) - 2 (10) == %4s (%2d)\n", numString, radix, valM2str, radix)
}

Output:

         101 ( 2) ==    5 (10)
101 ( 2) - 2 (10) ==   11 ( 2)
         101 ( 3) ==   10 (10)
101 ( 3) - 2 (10) ==   22 ( 3)
         101 ( 4) ==   17 (10)
101 ( 4) - 2 (10) ==   33 ( 4)
         101 ( 5) ==   26 (10)
101 ( 5) - 2 (10) ==   44 ( 5)
         101 ( 6) ==   37 (10)
101 ( 6) - 2 (10) ==   55 ( 6)
         101 ( 7) ==   50 (10)
101 ( 7) - 2 (10) ==   66 ( 7)
         101 ( 8) ==   65 (10)
101 ( 8) - 2 (10) ==   77 ( 8)
         101 ( 9) ==   82 (10)
101 ( 9) - 2 (10) ==   88 ( 9)
         101 (10) ==  101 (10)
101 (10) - 2 (10) ==   99 (10)
         101 (11) ==  122 (10)
101 (11) - 2 (10) ==   aa (11)
         101 (12) ==  145 (10)
101 (12) - 2 (10) ==   bb (12)
         101 (13) ==  170 (10)
101 (13) - 2 (10) ==   cc (13)
         101 (14) ==  197 (10)
101 (14) - 2 (10) ==   dd (14)
         101 (15) ==  226 (10)
101 (15) - 2 (10) ==   ee (15)
         101 (16) ==  257 (10)
101 (16) - 2 (10) ==   ff (16)
         101 (17) ==  290 (10)
101 (17) - 2 (10) ==   gg (17)
         101 (18) ==  325 (10)
101 (18) - 2 (10) ==   hh (18)
         101 (19) ==  362 (10)
101 (19) - 2 (10) ==   ii (19)
         101 (20) ==  401 (10)
101 (20) - 2 (10) ==   jj (20)
         101 (21) ==  442 (10)
101 (21) - 2 (10) ==   kk (21)
         101 (22) ==  485 (10)
101 (22) - 2 (10) ==   ll (22)
         101 (23) ==  530 (10)
101 (23) - 2 (10) ==   mm (23)
         101 (24) ==  577 (10)
101 (24) - 2 (10) ==   nn (24)
         101 (25) ==  626 (10)
101 (25) - 2 (10) ==   oo (25)
         101 (26) ==  677 (10)
101 (26) - 2 (10) ==   pp (26)
         101 (27) ==  730 (10)
101 (27) - 2 (10) ==   qq (27)
         101 (28) ==  785 (10)
101 (28) - 2 (10) ==   rr (28)
         101 (29) ==  842 (10)
101 (29) - 2 (10) ==   ss (29)
         101 (30) ==  901 (10)
101 (30) - 2 (10) ==   tt (30)
         101 (31) ==  962 (10)
101 (31) - 2 (10) ==   uu (31)
         101 (32) == 1025 (10)
101 (32) - 2 (10) ==   vv (32)
         101 (33) == 1090 (10)
101 (33) - 2 (10) ==   ww (33)
         101 (34) == 1157 (10)
101 (34) - 2 (10) ==   xx (34)
         101 (35) == 1226 (10)
101 (35) - 2 (10) ==   yy (35)
         101 (36) == 1297 (10)
101 (36) - 2 (10) ==   zz (36)

Haskell

Using built-in functions to convert integer into string, and vice versa, at any base up to 16:

Prelude> Numeric.showIntAtBase 16 Char.intToDigit 42 ""
"2a"
Prelude> fst $ head $ Numeric.readInt 16 Char.isHexDigit Char.digitToInt "2a"
42

It's actually more useful to represent digits internally as numbers instead of characters, because then one can define operations that work directly on this representation.

So conversion to and from digits represented as 0-9 and a-z is done in an additional step.

import Data.List
import Data.Char

toBase :: Int -> Int -> [Int]
toBase b v = toBase' [] v where
  toBase' a 0 = a
  toBase' a v = toBase' (r:a) q where (q,r) = v `divMod` b

fromBase :: Int -> [Int] -> Int
fromBase b ds = foldl' (\n k -> n * b + k) 0 ds

toAlphaDigits :: [Int] -> String
toAlphaDigits = map convert where
  convert n | n < 10    = chr (n + ord '0')
            | otherwise = chr (n + ord 'a' - 10)

fromAlphaDigits :: String -> [Int]
fromAlphaDigits = map convert where
 convert c | isDigit c = ord c - ord '0'
           | isUpper c = ord c - ord 'A' + 10
           | isLower c = ord c - ord 'a' + 10

Example:

*Main> toAlphaDigits $ toBase 16 $ 42
"2a"
*Main> fromBase 16 $ fromAlphaDigits $ "2a"
42


Or, to allow for digit variants like upper case vs lower case Hexadecimal, we can express our conversion function(s) in terms of a more general inBaseDigits function which, given an ordered list of digits as its first argument, returns an Int -> String unfold function. (The base is the length of the digit list).

If we want to assume a default character set, then a general toBase (Int -> Int -> String) can be also be derived from inBaseDigits.

import Data.Bifunctor (first)
import Data.List (unfoldr)
import Data.Tuple (swap)
import Data.Bool (bool)


inBaseDigits :: String -> Int -> String
inBaseDigits ds n =
  let base = length ds
  in reverse $
     unfoldr
       ((<*>)
          (bool Nothing . Just . first (ds !!) . swap . flip quotRem base)
          (0 <))
       n
 

inLowerHex :: Int -> String
inLowerHex = inBaseDigits "0123456789abcdef"
 
inUpperHex :: Int -> String
inUpperHex = inBaseDigits "0123456789ABCDEF"
 
inBinary :: Int -> String
inBinary = inBaseDigits "01"
 
inOctal :: Int -> String
inOctal = inBaseDigits "01234567"
 
inDevanagariDecimal :: Int -> String
inDevanagariDecimal = inBaseDigits "०१२३४५६७८९"
 
inHinduArabicDecimal :: Int -> String
inHinduArabicDecimal = inBaseDigits "٠١٢٣٤٥٦٧٨٩"
 
toBase :: Int -> Int -> String
toBase intBase n
  | (intBase < 36) && (intBase > 0) =
    inBaseDigits (take intBase (['0' .. '9'] ++ ['a' .. 'z'])) n
  | otherwise = []
 
main :: IO ()
main =
  mapM_ putStrLn $
  [ inLowerHex
  , inUpperHex
  , inBinary
  , inOctal
  , toBase 16
  , toBase 2
  , inDevanagariDecimal
  , inHinduArabicDecimal
  ] <*>
  [254]
Output:
fe
FE
11111110
376
fe
11111110
२५४
٢٥٤

HicEst

CHARACTER txt*80

    num = 36^7 -1                ! 7836416410
    CALL DecToBase(num, txt, 36)
    WRITE(ClipBoard, Name) num, txt, BaseToDec(36, txt)
 END

FUNCTION BaseToDec(base, string)
 CHARACTER string
    BaseToDec = 0
    length = LEN_TRIM(string)
    DO i = 1, length
      n = INDEX("0123456789abcdefghijklmnopqrstuvwxyz", string(i)) - 1
      BaseToDec = BaseToDec + n * base^(length-i)
    ENDDO
 END

SUBROUTINE DectoBase(decimal, string, base)
 CHARACTER string
    string = '0'
    temp = decimal
    length = CEILING( LOG(decimal+1, base) )
    DO i = length, 1, -1
      n = MOD( temp, base )
      string(i) = "0123456789abcdefghijklmnopqrstuvwxyz"(n+1)
      temp = INT(temp / base)
    ENDDO
 END
num=7836416410; txt=zzzzzzz; 7836416410;

Icon and Unicon

Icon and Unicon natively take integers in radix form for bases 2 through 36. There is no need to convert to integer as the value will be coerced when needed. However, a conversion routine is needed to convert integers back into radix form.

procedure main()
   every ( ns := "16r5a" | "-12r1a" ) & 
         ( b := 8 | 12 | 16 ) do {
         ns2 := convert(n := numeric(ns),b)
         printf("ns=%s -> n=%d -> %s\n",ns,n,ns2)
      }
end

link printf

procedure convert(i,b)                 #: convert i to base b radix representation
static digits
initial digits := &digits || &lcase

   i := integer(i) | runerr(101, i)    # arg/error checking
   /b := 10 | ( 2 < (b := integer(b)) <= *digits ) | runerr(205,b)

   if b = 10 then return i
   else {
      p := (s := "", (i := -(0 > i),"-")|"") || b || "r" # prefix/setup
      until i = 0 & *s > 0 do  
         s ||:= digits[1 + 1( i % b, i /:= b)]

      return p || reverse(s)
      }
end

printf.icn provides printf There are several conversion routines for bases in the IPL, however, none returns the input radix form.

Output:
ns=16r5a -> n=90 -> 8r132
ns=16r5a -> n=90 -> 12r76
ns=16r5a -> n=90 -> 16r5a
ns=-12r1a -> n=-22 -> -8r26
ns=-12r1a -> n=-22 -> -12r1a
ns=-12r1a -> n=-22 -> -16r16

J

J supports direct specification of native precision integers by base. The numbers are expressed as the base to be used (using base 10), the letter b, followed by the number itself. Following the initial letter b, other (lower case) letters represent "digts" 10 (a) through 35 (z), as in these examples:

   2b100 8b100 10b_100 16b100 36b100 36bzy
4 64 _100 256 1296 1294

Additionally, J has primitives #. and #: for dealing with base conversion issues.

Here are programs for conversion of numeric values to literals, and of literals to numbers:

numerals=: '0123456789abcdefghijklmnopqrstuvwxyz'
baseNtoL=: numerals {~ #.inv
baseLtoN=: [ #. numerals i. ]

Examples of use:

   2 baseNtoL 100 101
1100100
1100101
   16 baseNtoL 26
1a
   36 baseLtoN 'zy'
1294

These may be combined so the conversion performed is derived from the type of argument received.

   base=: baseNtoL :: baseLtoN
   
   16 base 'aa'
170
   16 base 170
aa

See also primary verbs Base and Antibase.

Java

for long's:

public static long backToTen(String num, int oldBase){
   return Long.parseLong(num, oldBase); //takes both uppercase and lowercase letters
}

public static String tenToBase(long num, int newBase){
   return Long.toString(num, newBase);//add .toUpperCase() for capital letters
}

for BigInteger's:

public static BigInteger backToTenBig(String num, int oldBase){
   return new BigInteger(num, oldBase); //takes both uppercase and lowercase letters
}

public static String tenBigToBase(BigInteger num, int newBase){
   return num.toString(newBase);//add .toUpperCase() for capital letters
}

JavaScript

ES5

k = 26
s = k.toString(16) //gives 1a
i = parseInt('1a',16) //gives 26
//optional special case for hex:
i = +('0x'+s) //hexadecimal base 16, if s='1a' then i=26.

Converts a number of arbitrary length from any base to any base Limitation: Any base or number that causes accumulator to overflow will lose precision!! Debugging or following the process is easy as it is kept in the expected base string format and order.

var baselist = "0123456789abcdefghijklmnopqrstuvwxyz", listbase = [];
for(var i = 0; i < baselist.length; i++) listbase[baselist[i]] = i; // Generate baselist reverse
function basechange(snumber, frombase, tobase)
{
 var i, t, to = new Array(Math.ceil(snumber.length * Math.log(frombase) / Math.log(tobase))), accumulator;
 if(1 < frombase < baselist.length || 1 < tobase < baselist.length) console.error("Invalid or unsupported base!");
 while(snumber[0] == baselist[0] && snumber.length > 1) snumber = snumber.substr(1); // Remove leading zeros character
 console.log("Number is", snumber, "in base", frombase, "to base", tobase, "result should be",
             parseInt(snumber, frombase).toString(tobase));
 for(i = snumber.length - 1, inexp = 1; i > -1; i--, inexp *= frombase)
  for(accumulator = listbase[snumber[i]] * inexp, t = to.length - 1; accumulator > 0 || t >= 0; t--)
  {
   accumulator += listbase[to[t] || 0];
   to[t] = baselist[(accumulator % tobase)  || 0];
   accumulator = Math.floor(accumulator / tobase);
  }
 return to.join('');
}
console.log("Result:", basechange("zzzzzzzzzz", 36, 10));

Using BigInteger, can convert any base.

// Tom Wu jsbn.js http://www-cs-students.stanford.edu/~tjw/jsbn/
var baselist = "0123456789abcdefghijklmnopqrstuvwxyz", listbase = [];
for(var i = 0; i < baselist.length; i++) listbase[baselist[i]] = i; // Generate baselist reverse
function baseconvert(snumber, frombase, tobase) // String number in base X to string number in base Y, arbitrary length, base
{
 var i, t, to, accum = new BigInteger(), inexp = new BigInteger('1', 10), tb = new BigInteger(),
     fb = new BigInteger(), tmp = new BigInteger();
 console.log("Number is", snumber, "in base", frombase, "to base", tobase, "result should be",
             frombase < 37 && tobase < 37 ? parseInt(snumber, frombase).toString(tobase) : 'too large');
 while(snumber[0] == baselist[0] && snumber.length > 1) snumber = snumber.substr(1); // Remove leading zeros
 tb.fromInt(tobase);
 fb.fromInt(frombase);
 for(i = snumber.length - 1, to = new Array(Math.ceil(snumber.length * Math.log(frombase) / Math.log(tobase))); i > -1; i--)
 {
  accum = inexp.clone();
  accum.dMultiply(listbase[snumber[i]]);
  for(t = to.length - 1; accum.compareTo(BigInteger.ZERO) > 0 || t >= 0; t--)
  {
   tmp.fromInt(listbase[to[t]] || 0);
   accum = accum.add(tmp);
   to[t] = baselist[accum.mod(tb).intValue()];
   accum = accum.divide(tb);
  }
  inexp = inexp.multiply(fb);
 }
 while(to[0] == baselist[0] && to.length > 1) to = to.slice(1); // Remove leading zeros
 return to.join('');
}

ES6

For more flexibility with digit variants (upper and lower case hex, digits in other languages/scripts etc) we can define toBase(intBase, n) in terms of a more general inBaseDigits(strDigits, n) which derives the base from the number of digits to be used.

(() => {
    'use strict';

    // toBase :: Int -> Int -> String
    const toBase = (intBase, n) =>
        intBase < 36 && intBase > 0 ?
        inBaseDigits('0123456789abcdef'.substr(0, intBase), n) : [];


    // inBaseDigits :: String -> Int -> [String]
    const inBaseDigits = (digits, n) => {
        const intBase = digits.length;

        return unfoldr(maybeResidue => {
                const [divided, remainder] = quotRem(maybeResidue.new, intBase);

                return {
                    valid: divided > 0,
                    value: digits[remainder],
                    new: divided
                };
            }, n)
            .reverse()
            .join('');
    };


    // GENERIC FUNCTIONS

    // unfoldr :: (b -> Maybe (a, b)) -> b -> [a]
    const unfoldr = (mf, v) => {
        var xs = [];
        return (until(
            m => !m.valid,
            m => {
                const m2 = mf(m);
                return (
                    xs = xs.concat(m2.value),
                    m2
                );
            }, {
                valid: true,
                value: v,
                new: v,
            }
        ), xs);
    };

    // curry :: ((a, b) -> c) -> a -> b -> c
    const curry = f => a => b => f(a, b);

    // until :: (a -> Bool) -> (a -> a) -> a -> a
    const until = (p, f, x) => {
        let v = x;
        while (!p(v)) v = f(v);
        return v;
    }

    // quotRem :: Integral a => a -> a -> (a, a)
    const quotRem = (m, n) => [Math.floor(m / n), m % n];

    // show :: a -> String
    const show = x => JSON.stringify(x, null, 2);


    // OTHER FUNCTIONS DERIVABLE FROM inBaseDigits

    // inLowerHex :: Int -> String
    const inLowerHex = curry(inBaseDigits)('0123456789abcdef');

    /// inUpperHex :: Int -> String
    const inUpperHex = curry(inBaseDigits)('0123456789ABCDEF');

    // inOctal :: Int -> String
    const inOctal = curry(inBaseDigits)('01234567');

    // inDevanagariDecimal :: Int -> String
    const inDevanagariDecimal = curry(inBaseDigits)('०१२३४५६७८९');


    // TESTS
    // testNumber :: [Int]
    const testNumbers = [255, 240];

    return testNumbers.map(n => show({
        binary: toBase(2, n),
        base5: toBase(5, n),
        hex: toBase(16, n),
        upperHex: inUpperHex(n),
        octal: inOctal(n),
        devanagariDecimal: inDevanagariDecimal(n)
    }));
})();
Output:
{
  "binary": "11111111",
  "base5": "2010",
  "hex": "ff",
  "upperHex": "FF",
  "octal": "377",
  "devanagariDecimal": "२५५"
}, {
  "binary": "11110000",
  "base5": "1430",
  "hex": "f0",
  "upperHex": "F0",
  "octal": "360",
  "devanagariDecimal": "२४०"
}

Joy

DEFINE
  digit == "0123456789abcdefghijklmnopqrstuvwxyz" of;
  itostr ==
    "" rollup
    [>=] [dup rollup div digit rotated swons rollup] while
    pop digit swons.

26 16 itostr.
"1a" 16 strtol.
Output:
"1a"
26

jq

# Convert the input integer to a string in the specified base (2 to 36 inclusive)
def convert(base):
  def stream:
    recurse(if . >= base then ./base|floor else empty end) | . % base ;
  [stream] | reverse
  | if   base <  10 then map(tostring) | join("")
    elif base <= 36 then map(if . < 10 then 48 + . else . + 87 end) | implode
    else error("base too large")
    end;

# input string is converted from "base" to an integer, within limits
# of the underlying arithmetic operations, and without error-checking:
def to_i(base):
  explode
  | reverse
  | map(if . > 96  then . - 87 else . - 48 end)  # "a" ~ 97 => 10 ~ 87
  | reduce .[] as $c
      # state: [power, ans]
      ([1,0]; (.[0] * base) as $b | [$b, .[1] + (.[0] * $c)])
  | .[1];

Example:

(255 | convert(16)),
 ("ff" | to_i(16)),
 ("10" | to_i(10))
Output:
$jq -M -r -n -f Non-decimal_radices.jq
ff
255
10

Julia

@show string(185, base=2)
@show string(185, base=3)
@show string(185, base=4)
@show string(185, base=5)
@show string(185, base=6)
@show string(185, base=7)
@show string(185, base=8)
@show string(185, base=9)
@show string(185, base=10)
@show string(185, base=11)
@show string(185, base=12)
@show string(185, base=13)
@show string(185, base=14)
@show string(185, base=15)
@show string(185, base=16)
Output:
string(185, base = 2) = "10111001"
string(185, base = 3) = "20212"
string(185, base = 4) = "2321"
string(185, base = 5) = "1220"
string(185, base = 6) = "505"
string(185, base = 7) = "353"
string(185, base = 8) = "271"
string(185, base = 9) = "225"
string(185, base = 10) = "185"
string(185, base = 11) = "159"
string(185, base = 12) = "135"
string(185, base = 13) = "113"
string(185, base = 14) = "d3"
string(185, base = 15) = "c5"
string(185, base = 16) = "b9"

Kotlin

An approach from first principles rather than using Java library functions:

Translation of: FreeBASIC
// version 1.0.6

fun min(x: Int, y: Int) = if (x < y) x else y

fun convertToBase(n: Int, b: Int): String {
    if (n < 2 || b < 2 || b == 10 || b > 36) return n.toString() // leave as decimal
    val sb = StringBuilder()
    var digit: Int
    var nn = n
    while (nn > 0) {
        digit = nn % b
        if (digit < 10) sb.append(digit)
        else            sb.append((digit + 87).toChar()) 
        nn /= b
    }
    return sb.reverse().toString()
}

fun convertToDecimal(s: String, b: Int): Int {
    if (b !in 2..36) throw IllegalArgumentException("Base must be between 2 and 36")
    if (b == 10) return s.toInt()
    val t = s.toLowerCase()
    var result = 0
    var digit: Int
    var multiplier = 1
    for (i in t.length - 1 downTo 0) {
        digit = -1
        if (t[i] >= '0' && t[i] <= min(57, 47 + b).toChar())
            digit = t[i].toInt() - 48
        else if (b > 10 && t[i] >= 'a' && t[i] <= min(122, 87 + b).toChar())
            digit = t[i].toInt() - 87
        if (digit == -1) throw IllegalArgumentException("Invalid digit present")
        if (digit > 0) result += multiplier * digit
        multiplier *= b
    }
    return result
}     

fun main(args: Array<String>) {
    for (b in 2..36) {
        val s = convertToBase(36, b)
        val f = "%2d".format(b)
        println("36 base $f = ${s.padEnd(6)} -> base $f = ${convertToDecimal(s, b)}")
    }
}
Output:
36 base  2 = 100100 -> base  2 = 36
36 base  3 = 1100   -> base  3 = 36
36 base  4 = 210    -> base  4 = 36
36 base  5 = 121    -> base  5 = 36
36 base  6 = 100    -> base  6 = 36
36 base  7 = 51     -> base  7 = 36
36 base  8 = 44     -> base  8 = 36
36 base  9 = 40     -> base  9 = 36
36 base 10 = 36     -> base 10 = 36
36 base 11 = 33     -> base 11 = 36
36 base 12 = 30     -> base 12 = 36
36 base 13 = 2a     -> base 13 = 36
36 base 14 = 28     -> base 14 = 36
36 base 15 = 26     -> base 15 = 36
36 base 16 = 24     -> base 16 = 36
36 base 17 = 22     -> base 17 = 36
36 base 18 = 20     -> base 18 = 36
36 base 19 = 1h     -> base 19 = 36
36 base 20 = 1g     -> base 20 = 36
36 base 21 = 1f     -> base 21 = 36
36 base 22 = 1e     -> base 22 = 36
36 base 23 = 1d     -> base 23 = 36
36 base 24 = 1c     -> base 24 = 36
36 base 25 = 1b     -> base 25 = 36
36 base 26 = 1a     -> base 26 = 36
36 base 27 = 19     -> base 27 = 36
36 base 28 = 18     -> base 28 = 36
36 base 29 = 17     -> base 29 = 36
36 base 30 = 16     -> base 30 = 36
36 base 31 = 15     -> base 31 = 36
36 base 32 = 14     -> base 32 = 36
36 base 33 = 13     -> base 33 = 36
36 base 34 = 12     -> base 34 = 36
36 base 35 = 11     -> base 35 = 36
36 base 36 = 10     -> base 36 = 36

LFE

Converting decimal numbers 26 and 3000 in LFE, using some different mechanisms:

> (: erlang list_to_integer '"1a" 16)
26
> #x1a
26
> (: erlang integer_to_list 26 16)
"1A"
> (: erlang list_to_integer '"101110111000" 2)
3000
> #b101110111000
3000
> (: erlang integer_to_list 3000 2)
"101110111000"

Liberty BASIC

   '   Base Converter v6

    global      alphanum$
    alphanum$   ="0123456789abcdefghijklmnopqrstuvwxyz"

    for i =1 to 20
    RandNum     =   int( 100 *rnd( 1))
    base        =2 +int( 35  *rnd( 1))

    print "Decimal "; using( "###", RandNum); " to base "; using( "###", base);_
         " is "; toBase$( base,  RandNum),_
         " back to dec. "; toDecimal( base, toBase$( base, RandNum))
    next i

    end '   ___________________________________________________________

    function toBase$( base, number) '   Convert decimal variable to number string.
        toBase$             =""
        for i =10 to 1 step -1
            remainder   =number mod base
            toBase$     =mid$( alphanum$, remainder +1, 1) +toBase$
            number      =int( number /base)
            if number <1 then exit for
        next i
    end function

    function toDecimal( base, s$)   '   Convert number string to decimal variable.
        toDecimal   =0
        for i =1 to len( s$)
            toDecimal =toDecimal *base +instr( alphanum$, mid$( s$, i, 1), 1) -1
        next i
    end function

Lua

Only had to write 'dec2base' as the reverse is provided by the in-built function 'tonumber'

function dec2base (base, n)
    local result = ""
    repeat
        local digit = n % base
        if digit > 9 then
            digit = string.char(digit + 87)
        end
        result = digit .. result
        n = n // base
    until n == 0
    return result
end

local x = dec2base(16, 26)
print(x)                    --> 1a
print(tonumber(x, 16))      --> 26

M2000 Interpreter

Module Checkit {
  k$=lambda$ (m, b as integer=16) -> {
    if b<2 or b>16 then error "base out of range"
    if m=0 then ="0" : exit
    z$="0123456789ABCDEF" 
    =lambda$ z$, b (m) ->{
      =if$(m=0->"", lambda$(m div b)+mid$(z$, m mod b + 1, 1))
    }(m)
  }
  k=lambda (m$, b as integer=16) -> {
    if b<2 or b>16 then error "base out of range"
    m$=trim$(m$)
    if m$="0" then =0 : exit
    z$="0123456789ABCDEF" 
    =lambda z$, b (m$) ->{
      =if(Len(m$)=0->0, lambda(mid$(m$,2))+(instr(z$, left$(m$,1))-1)*b**(len(m$)-1))
    }(m$)
  }
  Print k$(0)="0", k("0")=0
  Print k$(65535)="FFFF", k("FFFF", 16)=65535
  Print k$(0xF00F)="F00F", k("F00F", 16)=0xF00F
  Print k$(0xFFFFFFFF)="FFFFFFFF", k("FFFFFFFF", 16)=0xFFFFFFFF
  Print k$(100, 8)="144", k("144", 8)=100
  Print k$(100, 2)="1100100", k("1100100", 2)=100
}
Checkit

Output:

    True    True
    True    True
    True    True
    True    True
    True    True
    True    True


M4

eval(26,16)
define(`frombase',`eval(0r$2:$1)')
frombase(1a,16)

Output:

1a

26

Maple

#converts a number to a given based represented by a string
to_base := proc(num, based)
  local i;
  local chart := "0123456789abcdefghijklmnopqrstuvwxyz";
  local conversion := ListTools:-Reverse((convert(num,base,based)));
  local str := StringTools:-StringBuffer();
  for i in conversion do
    str:-append(chart[i+1]);
  end do;
  return str;
end proc:

#find the location of char in chart
find_digit := proc(char)
  if (StringTools:-HasAlpha(char)) then
    return (StringTools:-Ord(char) - 87);
  else 
    return (StringTools:-Ord(char) - 48);
  end if;
end proc:

#converts a string  with given base to a number
from_base := proc(str, base)
  local char;
  local result := 0;
  for char in str do
    result *= base;
    result += find_digit(char);
  end do;
  return result;
end proc:
Usage:
to_base(32, 11);
to_base(0, 16);
from_base("2a", 11);
from_base("1a",16);
Output:
"2a"
"0"
32
26

Mathematica/Wolfram Language

Use the built-in functions IntegerString[] and FromDigits[]:

IntegerString[26,16]
FromDigits["1a", 16])
Output:
"1a"
26

MATLAB / Octave

Use the built-in functions base2dec() and dec2base():

dec2base(26,16)
base2dec('1a', 16)

Output:

1A

26

МК-61/52

П8  ->  1 0 П0  ПП  13  ИП7 П0  ИП8
ПП  13  С/П П7  ->  П6  ->  1 П4  П5
Сx  <-> ^ ПП  68  П3  - ИП7 * П2
ПП  68  ИП4 ИП6 * П4  / + ИП2 ИП1
- x#0 45  L0  27  ->  ИП3 ^ ИП7 /
ПП  68  ИП7 * - ИП5 * + ИП5 ИП6
* П5  ->  ИП1 x=0 47  ->  В/О 1 +
П1  КИП1  ->  ->  ИП1 В/О

Input: Nm ^ m ^ n В/О С/П.

Output: Nn -> PX.

NetRexx

In NetRexx numbers are held as Rexx strings so you can take advantage of Java's BigInteger to do radix conversions.

/* NetRexx */
options replace format comments java crossref symbols nobinary

import java.math.BigInteger

numeric digits 200

parse arg input -- input should be val, radix; no input results in using default test data
-- test data - number pairs where 1st is value and 2nd is target radix
inputs = [ -
  '1234,         10', '01234,  8', 'fe,  16', 'f0e,   16', -
  '0,            10', '00,     2', '11,   2', '070,    8', -
  '77,            8', 'f0e,   16', '070, 16', '0xf0e, 36', -
  '000999ABCXYZ, 36', 'ff,    36', 'f,   16', 'z,     37'  -
  ]
if input.length() > 0 then inputs = [input] -- replace test data with user input

loop i_ = 0 to inputs.length - 1
  do
    in = inputs[i_]
    parse in val . ',' radix .
    valB = toDecimal(val, radix)        -- NetRexx default is to store digits as Rexx strings
    valD = fromDecimal(valB + 0, radix) -- Add zero just to prove the result treated as a number
    say val.right(16)'['radix.right(2, 0)']:' valB.right(16)'[10] ==' valD.right(16)'['radix.right(2, 0)']'
  catch nx = NumberFormatException
    say 'Error -- Input:' val', radix:' radix
    nx.printStackTrace()
  end
  end i_

return

method toDecimal(val = String, radix = int 10) public static returns Rexx
  bi = BigInteger(val, radix)
  return bi.toString()

method fromDecimal(val = String, radix = int 10) public static returns Rexx
  bi = BigInteger(val.toString(), 10)
  return bi.toString(radix)

Output:

            1234[10]:             1234[10] ==             1234[10]
           01234[08]:              668[10] ==             1234[08]
              fe[16]:              254[10] ==               fe[16]
             f0e[16]:             3854[10] ==              f0e[16]
               0[10]:                0[10] ==                0[10]
              00[02]:                0[10] ==                0[02]
              11[02]:                3[10] ==               11[02]
             070[08]:               56[10] ==               70[08]
              77[08]:               63[10] ==               77[08]
             f0e[16]:             3854[10] ==              f0e[16]
             070[16]:              112[10] ==               70[16]
           0xf0e[36]:          1559102[10] ==             xf0e[36]
    000999ABCXYZ[36]:   26115481426427[10] ==        999abcxyz[36]
              ff[36]:              555[10] ==               ff[36]
               f[16]:               15[10] ==                f[16]
Error -- Input: z, radix: 37
java.lang.NumberFormatException: Radix out of range
  at java.math.BigInteger.<init>(BigInteger.java:294)
  at RNonDecRadixConvert.toDecimal(RNonDecRadixConvert.nrx:77)
  at RNonDecRadixConvert.main(RNonDecRadixConvert.nrx:57)

Nim

import strutils

proc reverse(a: string): string =
  result = newString(a.len)
  for i, c in a:
    result[a.high - i] = c

const digits = "0123456789abcdefghijklmnopqrstuvwxyz"

proc toBase[T](num: T, base: range[2..36]): string =
  if num == 0: return "0"
  result = ""
  if num < 0: result.add '-'
  var tmp = abs(num)
  var s = ""
  while tmp > 0:
    s.add digits[int(tmp mod base)]
    tmp = tmp div base
  result.add s.reverse

proc fromBase(str: string, base: range[2..36]): BiggestInt =
  var str = str
  let first = if str[0] == '-': 1 else: 0

  for i in first .. str.high:
    let c = str[i].toLowerAscii
    assert c in digits[0 ..< base]
    result = result * base + digits.find c

  if first == 1: result *= -1

echo 26.toBase 16
echo "1a".fromBase 16

Output:

1a
26

OCaml

let int_of_basen n str =
  match n with
  | 16 -> int_of_string("0x" ^ str)
  |  2 -> int_of_string("0b" ^ str)
  |  8 -> int_of_string("0o" ^ str)
  | _ -> failwith "unhandled"

let basen_of_int n d =
  match n with
  | 16 -> Printf.sprintf "%x" d
  |  8 -> Printf.sprintf "%o" d
  | _ -> failwith "unhandled"
# basen_of_int 16 26 ;;
- : string = "1a"

# int_of_basen 16 "1a" ;;
- : int = 26

A real base conversion implementation:

let basen_of_int b n : string =
  let tab = "0123456789abcdefghijklmnopqrstuvwxyz" in
  let rec aux x l =
    if x < b
    then tab.[x] :: l
    else aux (x / b) (tab.[x mod b] :: l)
  in
  String.of_seq (List.to_seq (aux n []))

let basen_to_int b ds : int =
  let of_sym c =
    int_of_char c - match c with
    | '0' .. '9' -> int_of_char '0'
    | 'a' .. 'z' -> int_of_char 'a' - 10
    | 'A' .. 'Z' -> int_of_char 'A' - 10
    | _ -> invalid_arg "unkown digit"
  in
  String.fold_left (fun n d -> n * b + of_sym d) 0 ds

Example:

# basen_of_int 16 26;;
- : string = "1a"
# basen_to_int 16 "1a";;
- : int = 26

PARI/GP

toBase(n,b)={
  my(s="",t);
  while(n,
    t=n%b;
    n\=b;
    s=Str(if(t<=9,t,Strchr(Vecsmall([87+t]))),s)
  );
  if(#s,s,"0")
};
fromBase(s,b)={
  my(t=0);
  s=Vecsmall(s);
  for(i=1,#s,1,
    t=b*t+s[i]-if(s[i]<58,48,87)
  );
  t
};

Pascal

Works with: Free_Pascal
Program ConvertDemo(output);

uses
  Math, SysUtils;

const
  alphanum = '0123456789abcdefghijklmnopqrstuvwxyz';

function ToDecimal(base: integer; instring: string): integer;
  var
    inlength, i, n: integer;
  begin 
    ToDecimal := 0;
    inlength := length(instring);
    for i := 1 to inlength do
    begin
      n := pos(instring[i], alphanum) - 1;
      n := n * base**(inlength-i);
      Todecimal := ToDecimal + n;
    end;
  end;

function ToBase(base, number: integer): string;
  var
    i, rem: integer;
  begin
    ToBase :='                               ';
    for i := 31 downto 1 do
    begin
      if (number < base) then
      begin
        ToBase[i] := alphanum[number+1];
        break;
      end;
      rem := number mod base;
      ToBase[i] := alphanum[rem+1];
      number := number div base;
    end;
    ToBase := trimLeft(ToBase);
  end;

begin
  writeln ('1A: ', ToDecimal(16, '1a'));
  writeln ('26: ', ToBase(16, 26));
end.

Output:

% ./Convert
1A: 26
26: 1a

Perl

For base 2 and 16, we can do this entirely with language features:

sub to2  { sprintf "%b", shift; }
sub to16 { sprintf "%x", shift; }
sub from2  { unpack("N", pack("B32", substr("0" x 32 . shift, -32))); }
sub from16 { hex(shift); }

Small functions will handle arbitrary base conversions for bases 2-36:

sub base_to {
  my($n,$b) = @_;
  my $s = "";
  do {
    $s = ('0'..'9','a'..'z')[$n % $b] . $s
  } while $n = int($n / $b);
  $s
}
sub base_from {
  my($n,$b) = @_;
  my $t = 0;
  for my $c (split(//, lc($n))) {
    $t = $b * $t + index("0123456789abcdefghijklmnopqrstuvwxyz", $c);
  }
  $t;
}

There are a plethora of modules that perform base conversion.

The core POSIX module includes strtol (and strtoul) which is simple and fast, but only does conversions from a base. On some platforms the function may be limited to 32-bit even with a 64-bit Perl.

use POSIX;
my ($num, $n_unparsed) = strtol('1a', 16);
$n_unparsed == 0 or die "invalid characters found";
print "$num\n"; # prints "26"
The ntheory module includes functions that will perform base conversion, and is fast. It supports bases up to 36 and bigints.
Library: ntheory
use ntheory qw/fromdigits todigitstring/;
my $n   = 65261;
my $n16 = todigitstring($n, 16) || 0;
my $n10 = fromdigits($n16, 16);
say "$n $n16 $n10";  # prints "65261 feed 65261"

Other modules include but are not limited to:

The last two are much slower than the others or the simple functions above, but may have extra features. Math::Base::Convert and Convert::BaseN are currently not recommended.

The module Math::Fleximal not only does very arbitrary base conversion, but allows computations in different bases.

Phix

Phix itself handles number input in the expected decimal, or binary, octal, hexadecimal, and any base from 2 to 36 using prefixes 0b, 0o, 0x/X/#, and 0(2..36)
The (s)printf() routine can generate strings in decimal, binary, octal, hexadecimal, or base 2-36|62, using %d/e/f/g, %b, %o, %x/X, %a|A formats respectively.
The builtin to_number() function has an inbase parameter which defaults to 10 but can be 2..62.
Note however that only decimal fractions are supported in the core language itself, and to_number(), and that (s)printf's %d..A are all integer-only, and %e/f/g decimal-only.
Also note that 0t is(/was) an alternative for 0o (octal) on desktop/Phix, but not supported by JavaScript and hence pwa/p2js.
mpz_set_str() and mpfr_set_str() can handle input strings expressed in decimal, binary (0b prefix), hexadecimal (0x prefix), or bases 2..62, including non-decimal fractions.
mpz_get_str(), mpfr_get_str() [desktop/Phix only], and mpfr_get_fixed() can generate output strings in all bases 2..62.

with javascript_semantics
?{26,0b11010,0o32,0x1A,0X1a,#1A,0(16)1A}        -- displays {26,26,26,26,26,26,26}
printf(1,"%d == 0b%b == 0x%x\n",26)             -- displays 26 == 0b11010 == 0x1A
printf(1,"%d == o(62)%A\n",{26,{62,26}})        -- displays 26 == 0(62)Q
?to_number("1a",{},16)                          -- displays 26
include mpfr.e
mpfr f = mpfr_init()
mpfr_set_str(f,"110.01",2)
printf(1,"0b%s == %s\n",{mpfr_get_fixed(f,0,2),mpfr_get_fixed(f)}) -- 0b110.01 == 6.25

The following (given the above not necessarily very useful) routines can handle simple integer conversions, in bases 2 to 36.
You are expected to strip any leading "#" or "0x" from hexadecimal input strings (etc) manually, and (as-is) only use a-z not A-Z.

-- demo\rosetta\Convert_base.exw
function to_base(integer i, base)
    sequence s = ""
    while i>0 do
        integer c = remainder(i,base)
        s = prepend(s,c+iff(c<10?'0':'a'-10))
        i = floor(i/base)
    end while
    if length(s)=0 then s = "0" end if
    return s
end function
 
function from_base(string s, integer base)
    integer res = 0
    for i=1 to length(s) do
        integer c = s[i]
        res = res*base+(c-iff(c<='9'?'0':'a'-10))
    end for
    return res
end function
 
?to_base(256,16)
?from_base("100",16)
Output:
"100"
256

PHP

PHP has a base_convert() function that directly converts between strings of one base and strings of another base:

base_convert("26", 10, 16); // returns "1a"

If you want to convert a string to an integer, the intval() function optionally takes a base argument when given a string:

intval("1a", 16); // returns 26

To go the other way around, I guess you can use base_convert() again; I am unaware of a better way:

base_convert(26, 10, 16); // returns "1a"

In addition, there are specialized functions for converting certain bases:

// converts int to binary string
decbin(26); // returns "11010"
// converts int to octal string
decoct(26); // returns "32"
// converts int to hex string
dechex(26); // returns "1a"
// converts binary string to int
bindec("11010"); // returns 26
// converts octal string to int
octdec("32"); // returns 26
// converts hex string to int
hexdec("1a"); // returns 26

PicoLisp

(de numToString (N Base)
   (default Base 10)
   (let L NIL
      (loop
         (let C (% N Base)
            (and (> C 9) (inc 'C 39))
            (push 'L (char (+ C `(char "0")))) )
         (T (=0 (setq N (/ N Base)))) )
      (pack L) ) )

(de stringToNum (S Base)
   (default Base 10)
   (let N 0
      (for C (chop S)
         (when (> (setq C (- (char C) `(char "0"))) 9)
            (dec 'C 39) )
         (setq N (+ C (* N Base))) )
      N ) )

(prinl (numToString 26 16))
(prinl (stringToNum "1a" 16))
(prinl (numToString 123456789012345678901234567890 36))

Output:

"1a"
26
"byw97um9s91dlz68tsi"

PL/I

convert: procedure (N, base) returns (character (64) varying) recursive;
   declare N fixed binary (31), base fixed binary;
   declare table (0:15) character (
      '0', '1', '2', '3', '4', '5', '6', '7',
      '8', '9', 'a', 'b', 'c', 'd', 'e', 'f');
   declare s character (64) varying;

   if N = 0 then return ('');

   s = convert(N/base, base);
   return (s || table(mod(N, base)) );
end convert;

PL/M

100H:

/* CONVERT A NUMBER TO A GIVEN BASE */
TO$BASE: PROCEDURE (N, BASE, BUF) ADDRESS;
    DECLARE (N, BUF, I, J, K) ADDRESS;
    DECLARE (D, BASE, STR BASED BUF) BYTE;
    
    /* GENERATE DIGITS */
    I = 0;
DIGIT:
    D = N MOD BASE;
    N = N / BASE;
    IF D < 10 THEN STR(I) = D + '0';
    ELSE STR(I) = (D - 10) + 'A';
    I = I + 1;
    IF N > 0 THEN GO TO DIGIT;
    
    /* PUT DIGITS IN HIGH-ENDIAN ORDER */
    J = 0;
    K = I-1;
    DO WHILE (J < K);
        D = STR(K);
        STR(K) = STR(J);
        STR(J) = D;
        K = K-1;
        J = J+1;
    END;
    
    STR(I) = '$';
    RETURN BUF;
END TO$BASE;


/* READ A NUMBER IN A GIVEN BASE */
FROM$BASE: PROCEDURE (BUF, BASE) ADDRESS;
    DECLARE (BUF, RESULT) ADDRESS;
    DECLARE (D, BASE, CHAR BASED BUF) BYTE;
    
    RESULT = 0;
    DO WHILE CHAR <> '$';
        D = CHAR - '0';
        IF D >= 10 THEN D = D - ('A' - '0') + 10;
        RESULT = (RESULT * BASE) + D;
        BUF = BUF + 1;
    END;
    RETURN RESULT;
END FROM$BASE;

/* CP/M BDOS ROUTINES */
BDOS: PROCEDURE (F,A); DECLARE F BYTE, A ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
CRLF: PROCEDURE; CALL PRINT(.(13,10,'$')); END CRLF;

/* EXAMPLES */
DECLARE I BYTE, N ADDRESS;

CALL PRINT(.'1234 IN BASES 2-36: $'); CALL CRLF;
DO I=2 TO 36;
    CALL PRINT(.'BASE $');
    CALL PRINT(TO$BASE(I, 10, .MEMORY));
    CALL PRINT(.(': ',9,'$'));
    CALL PRINT(TO$BASE(1234, I, .MEMORY));
    CALL CRLF;
END;

CALL PRINT(.'''25'' IN BASES 10-36: $'); CALL CRLF;
DO I=10 TO 36;
    CALL PRINT(.'BASE $');
    CALL PRINT(TO$BASE(I, 10, .MEMORY));
    CALL PRINT(.(':',9,'$'));
    N = FROM$BASE(.'25$', I);
    CALL PRINT(TO$BASE(N, 10, .MEMORY));
    CALL CRLF;
END;

CALL EXIT;
EOF
Output:
1234 IN BASES 2-36:
BASE 2:         10011010010
BASE 3:         1200201
BASE 4:         103102
BASE 5:         14414
BASE 6:         5414
BASE 7:         3412
BASE 8:         2322
BASE 9:         1621
BASE 10:        1234
BASE 11:        A22
BASE 12:        86A
BASE 13:        73C
BASE 14:        642
BASE 15:        574
BASE 16:        4D2
BASE 17:        44A
BASE 18:        3EA
BASE 19:        37I
BASE 20:        31E
BASE 21:        2GG
BASE 22:        2C2
BASE 23:        27F
BASE 24:        23A
BASE 25:        1O9
BASE 26:        1LC
BASE 27:        1IJ
BASE 28:        1G2
BASE 29:        1DG
BASE 30:        1B4
BASE 31:        18P
BASE 32:        16I
BASE 33:        14D
BASE 34:        12A
BASE 35:        109
BASE 36:        YA
'25' IN BASES 10-36:
BASE 10:        25
BASE 11:        27
BASE 12:        29
BASE 13:        31
BASE 14:        33
BASE 15:        35
BASE 16:        37
BASE 17:        39
BASE 18:        41
BASE 19:        43
BASE 20:        45
BASE 21:        47
BASE 22:        49
BASE 23:        51
BASE 24:        53
BASE 25:        55
BASE 26:        57
BASE 27:        59
BASE 28:        61
BASE 29:        63
BASE 30:        65
BASE 31:        67
BASE 32:        69
BASE 33:        71
BASE 34:        73
BASE 35:        75
BASE 36:        77

Pop11

Pop11 can input and output routines can use any base up to 36 (depending on value 'pop_pr_radix' variable). 'radix_apply' runs i/o routine temporarly setting 'pop_pr_radix' to given value. 'sprintf' procedure instead of printing returns string. So, to convert number to given value we just compose built-in procedures:

define number_to_base(n, base);
    radix_apply(n, '%p', sprintf, base);
enddefine;

In input base optionally preceeds the number, for example 8:15 is 13. So, to convert string in given base we need to prepend base prefix and read number from string:

define string_in_base_to_number(s, base);
    incharitem(stringin(base >< ':' >< s))();
enddefine;

PureBasic

Global alphanum$ = "0123456789abcdefghijklmnopqrstuvwxyz" ;36 digits
#maxIntegerBitSize = SizeOf(Integer) * 8
 
Procedure toDecimal(base, s.s)
  Protected length, i, toDecimal
  
  length = Len(s)
  If length: toDecimal = FindString(alphanum$, Left(s, 1), 1) - 1: EndIf 
  
  For i = 2 To length
    toDecimal * base + FindString(alphanum$, Mid(s, i, 1), 1) - 1
  Next
  ProcedureReturn toDecimal
EndProcedure
 
Procedure.s toBase(base, number)
  Protected i, rem, toBase.s{#maxIntegerBitSize} = Space(#maxIntegerBitSize) 
  
  For i = #maxIntegerBitSize To 1 Step -1
    rem = number % base
    PokeC(@toBase + i - 1, PeekC(@alphanum$ + rem))
    If number < base: Break: EndIf 
    number / base
  Next
  ProcedureReturn LTrim(toBase)
EndProcedure

If OpenConsole()
  PrintN( Str(toDecimal(16, "1a")) )
  
  PrintN( toBase(16, 26) )
  
  Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
  Input()
  CloseConsole()
EndIf

Sample output:

26
1a

Python

Python: string to number

Converting from string to number is straight forward:

i = int('1a',16)  # returns the integer 26

Python: number to string

Converting from number to string is harder:

Recursive
digits = "0123456789abcdefghijklmnopqrstuvwxyz"
def baseN(num, b):
    return digits[num] if num < b else baseN(num // b, b) + digits[num % b]
Iterative
digits = "0123456789abcdefghijklmnopqrstuvwxyz"

def baseN(num, b):
    result = []
    while num >= b:
        num, d = divmod(num, b)
        result.append(digits[d])
    result.append(digits[num])
    return ''.join(result[::-1])
Sample run from either
In [1: baseN(26, 16)
Out[1]: '1a'

Quackery

Handles radices in the range 2 to 36.

  [ base put 
    number$
    base release
    $ "" swap
    witheach 
      [ lower join ] ] is base_to_string ( n n --> $ )

  [ base put
    $->n drop
    base release ]     is string_to_base ( $ n --> n )
Output:

As a dialogue in the quackery shell.

/O> $ "sesquipedalian" 36 string_to_base
... 

Stack: 4846409295160778886623 

/O> 36 base_to_string echo$ cr
... 
sesquipedalian

Stack empty.

R

int2str <- function(x, b) {
  if(x==0) return("0")
  if(x<0) return(paste0("-", base(-x,b)))
  
  map <- c(as.character(0:9), letters)
  res <- ""
  while (x>0) {
    res <- c(map[x %% b + 1], res)
    x <- x %/% b
  }
  return(paste(res, collapse=""))
}

str2int <- function(s, b) {
  map <- c(as.character(0:9), letters)
  s <- strsplit(s,"")[[1]]
  res <- sapply(s, function(x) which(map==x))
  res <- as.vector((res-1) %*% b^((length(res)-1):0))
  return(res)
}

## example: convert 255 to hex (ff):
int2str(255, 16)

## example: convert "1a" in base 16 to integer (26):
str2int("1a", 16)

Racket

#lang racket

;; Both assume valid inputs
(define (num->str N r)
  (let loop ([N N] [digits '()])
    (define-values [N1 d] (quotient/remainder N r))
    (define digits1 (cons (integer->char (+ d (if (< d 10) 48 55))) digits))
    (if (zero? N) (list->string digits1) (loop N1 digits1))))
(define (str->num S r)
  (for/fold ([N 0])
            ([B (string->bytes/utf-8 (string-upcase S))])
    (+ (* N r) (- B (if (< 64 B) 55 48)))))

;; To try it out:
(define (random-test)
  (define N (random 1000000))
  (define r (+ 2 (random 35)))
  (define S (num->str N r))
  (define M (str->num S r))
  (printf "~s -> ~a#~a -> ~a => ~a\n" N S r M (if (= M N) 'OK 'BAD)))
;; (random-test)

Raku

(formerly Perl 6)

sub from-base(Str $str, Int $base) {
    +":$base\<$str>";
}

sub to-base(Real $num, Int $base) {
    $num.base($base);
}

These work on any real type including integer types.

REXX

Instead of writing two separate routines, only one was written to handle both tasks.

This routine was ripped out from a bigger version of mine that allowed any number as input, including decimal fractions (or whatever base).

Illegal numerals/digits are detected as well as illegal (or unsupported) bases.

No   number-conversion   BIFs   (Built-In Functions)   were used in this REXX program.

        ┌────────────────────────────────────────────────────────────────────┐
      ┌─┘ Input to this program     (bases must be positive integers > 1):   └─┐
      │                                                                        │
      │                       x        is required  (it may have a sign).      │
      │                     toBase     the base to convert   X   to.           │
      │                     inBase     the base  X  is expressed in.           │
      │                                                                        │
      │  If  X  has a leading sign,  it is maintained (kept) after conversion. │
      │                                                                        │
      │  toBase   or   inBase    can be a comma (,)  which causes the default  │
      └─┐ of  10  to be used.    The limits of bases are:    2 ──► 90.       ┌─┘
        └────────────────────────────────────────────────────────────────────┘
/*REXX program converts integers from  one base  to  another   (using bases  2 ──► 90). */
@abc = 'abcdefghijklmnopqrstuvwxyz'              /*lowercase (Latin or English) alphabet*/
parse  upper  var  @abc    @abcU                 /*uppercase a version of   @abc.       */
@@ = 0123456789 || @abc || @abcU                 /*prefix them with all numeric digits. */
@@ = @@'<>[]{}()?~!@#$%^&*_=|\/;:¢¬≈'            /*add some special characters as well. */
                                                 /* [↑]  all characters must be viewable*/
numeric digits 3000                              /*what da hey, support gihugeic numbers*/
maxB= length(@@)                                 /*max base/radix supported in this code*/
parse arg x toB inB 1 ox . 1 sigX 2 x2 .         /*obtain:  three args, origX, sign ··· */
if pos(sigX, "+-")\==0  then    x= x2            /*does X have a leading sign (+ or -) ?*/
                        else sigX=               /*Nope. No leading sign for the X value*/
if   x==''             then call erm             /*if no  X  number, issue an error msg.*/
if toB=='' | toB==","  then toB= 10              /*if skipped, assume the default (10). */
if inB=='' | inB==","  then inB= 10              /* "    "        "    "     "      "   */
if inB<2   | inB>maxB  | \datatype(inB, 'W')  then call erb  "inBase "  inB
if toB<2   | toB>maxB  | \datatype(toB, 'W')  then call erb  "toBase "  toB
#=0                                              /*result of converted  X  (in base 10).*/
      do j=1  for length(x)                      /*convert  X:   base inB  ──► base 10. */
      ?= substr(x,j,1)                           /*pick off a numeral/digit from  X.    */
      _= pos(?, @@)                              /*calculate the value of this numeral. */
      if _==0 | _>inB  then call erd x           /*is  _  character an illegal numeral? */
      #= # * inB   +   _   -   1                 /*build a new number,  digit by digit. */
      end    /*j*/                               /* [↑]  this also verifies digits.     */
y=                                               /*the value of   X   in   base  B.     */
      do  while  # >= toB                        /*convert #:    base 10  ──►  base toB.*/
      y= substr(@@, (#//toB) + 1, 1)y            /*construct the output number.         */
      #= # % toB                                 /*      ··· and whittle  #  down also. */
      end    /*while*/                           /* [↑]  algorithm may leave a residual.*/
                                                 /* [↓]         Y  is the residual.     */
y= sigX || substr(@@, #+1, 1)y                   /*prepend the sign  if  it existed.    */
say ox  "(base"       inB')'       center("is", 20)       y       '(base'       toB")"
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
erb:  call ser  'illegal'   arg(1)",  it must be in the range:  2──►"maxB
erd:  call ser  'illegal digit/numeral  ['?"]  in:  "       x
erm:  call ser  'no argument specified.'
ser:  say; say  '***error!***';         say arg(1);             exit 13
output   when input is expressed in hexadecimal   (maximum positive integer in a signed 32-bit word):     7fffffff   ,   16
7fffffff (base 16)          is          2147483647 (base 10)
output   when input used (expressed in decimal) is:     4095   2
4095 (base 10)          is          111111111111 (base 2)
output   when input used (expressed in binary) is:     100   3   2
100 (base 2)          is          11 (base 3)
output   when input used (expressed in base 62) is:     zombiesAreEatingDeadVegetables   10   62
zombiesAreEatingDeadVegetables (base 62)          is          337500751396688020801073824403268172711989016896916476 (base 10)

Ring

# Project : Non-decimal radices/Convert

see "0 (decimal) -> " + hex(0) + " (base 16)" + nl
see "26 (decimal) -> " + hex(26) + " (base 16)" + nl
see "383 (decimal) -> " + hex(383) + " (base 16)" + nl
see "26 (decimal) -> " + tobase(26, 2) + " (base 2)" + nl
see "383 (decimal) -> " + tobase(383, 2)  + " (base 2)" + nl
see "1a (base 16) -> " + dec("1a") + " (decimal)" + nl
see "1A (base 16) -> " + dec("1A") + " (decimal)" + nl
see "17f (base 16) -> " + dec("17f") + " (decimal)" + nl
see "101111111 (base 2) -> " + bintodec("101111111") + " (decimal)" + nl
 
func tobase(nr, base) 
     binary = 0
     i = 1  
     while(nr != 0) 
           remainder = nr % base
           nr = floor(nr/base)
           binary= binary + (remainder*i)
           i = i*10
     end
     return string(binary)
 
func bintodec(bin)
     binsum = 0
     for n=1  to len(bin)
         binsum = binsum + number(bin[n]) *pow(2, len(bin)-n)
     next
     return binsum

Output:

0 (decimal) -> 0 (base 16)
26 (decimal) -> 1a (base 16)
383 (decimal) -> 17f (base 16)
26 (decimal) -> 11010 (base 2)
383 (decimal) -> 101111111 (base 2)
1a (base 16) -> 26 (decimal)
1A (base 16) -> 26 (decimal)
17f (base 16) -> 383 (decimal)
101111111 (base 2) -> 383 (decimal)

RPL

≪ → base 
  ≪ "" SWAP 
     WHILE DUP REPEAT 
        base MOD LAST / FLOOR 
        SWAP DUP 9 > 87 48 IFTE + CHR 
        ROT + SWAP 
     END DROP
 ≫   ≫  ‘D→B’ STO

≪ → number base 
  ≪ 0 1 number SIZE FOR j 
       base * number j DUP SUB 
       NUM DUP 57 > 87 48 IFTE - + 
    NEXT 
≫ ≫ ‘B→D’ STO
"r0setta" 36 B→D
DUP 36 D→B
Output:
2: 58820844142
1: "r0setta"

Ruby

This converts strings from any base to any base up to base 36.

class String
  def convert_base(from, to)
    Integer(self, from).to_s(to)  
    # self.to_i(from).to_s(to) #if you don't want exceptions
  end
end

# first three taken from TCL
p "12345".convert_base(10, 23) # => "107h"
p "107h".convert_base(23, 7) # =>"50664"
p "50664".convert_base(7, 10) # =>"12345"
p "1038334289300125869792154778345043071467300".convert_base(10, 36) # =>"zombieseatingdeadvegetables"
p "ff".convert_base(15, 10) # => ArgumentError

Run BASIC

global    basCvt$
basCvt$   ="0123456789abcdefghijklmnopqrstuvwxyz"
html "<table border=1><tr bgcolor=wheat align=center><td>Decimal</td><td>To Base</td><td>Num</td><td>to Dec</td></tr>"

for i =1 to 10
  RandNum     =    int(100 * rnd(1))
  base        = 2 +int(35  * rnd(1))
 
  html "<tr align=right><td>";using("###", RandNum);"</td><td>";using("###", base);"</td><td>";toBase$(base,RandNum);"</td><td>";toDecimal( base, toBase$( base, RandNum));"</td></tr>"
next i
html "</table>"
end 

function toBase$(b,n) '   b=base n=nmber
  toBase$             =""
  for i =10 to 1 step -1
     toBase$     =mid$(basCvt$,n mod b +1,1) +toBase$
    n      =int( n /b)
    if n <1 then exit for
  next i
end function
 
function toDecimal( b, s$)   '   scring number to decimal
  toDecimal   =0
  for i =1 to len( s$)
    toDecimal = toDecimal * b + instr(basCvt$,mid$(s$,i,1),1) -1
  next i
end function
DecimalTo BaseNumto Dec
51 211001151
27 102727
12 18c12
90 352k90
99 175e99
99 185999
55 115055
56 282056
71 342371
61 232f61

Rust

Rust standard library provides parsing a string in a given radix to all integer types. There is no reverse operation (except for format specifiers for binary, octal, decimal and hexadecimal base).

fn format_with_radix(mut n: u32, radix: u32) -> String {
    assert!(2 <= radix && radix <= 36);

    let mut result = String::new();

    loop {
        result.push(std::char::from_digit(n % radix, radix).unwrap());
        n /= radix;
        if n == 0 {
            break;
        }
    }

    result.chars().rev().collect()
}

#[cfg(test)]
#[test]
fn test() {
    for value in 0..100u32 {
        for radix in 2..=36 {
            let s = format_with_radix(value, radix);
            let v = u32::from_str_radix(s.as_str(), radix).unwrap();
            assert_eq!(value, v);
        }
    }
}

fn main() -> Result<(), Box<dyn std::error::Error>> {
    println!("{}", format_with_radix(0xdeadbeef, 2));
    println!("{}", format_with_radix(0xdeadbeef, 36));
    println!("{}", format_with_radix(0xdeadbeef, 16));
    println!("{}", u32::from_str_radix("DeadBeef", 16)?);
    Ok(())
}

Scala

def backToBig(num: String, oldBase: Int): BigInt = BigInt(num, oldBase)

def bigToBase(num: BigInt, newBase: Int): String = num.toString(newBase)

Scheme

R7RS specifies only a radix of 2, 8, 10, or 16 for the functions below. However, some implementations support arbitrary (e.g. Chibi-Scheme or Guile).

(number->string 26 16)

(string->number "1a" 16)

Seed7

The type integer defines the operator radix and the function integer, which convert to string and vice versa. The type bigInteger defines radix and bigInteger for corresponding purposes.

$ include "seed7_05.s7i";
  include "bigint.s7i";
 
const proc: main is func
  begin
    writeln(60272032366_ radix 36);      # Convert bigInteger to string
    writeln(591458 radix 36);            # Convert integer to string

    writeln(bigInteger("rosetta", 36));  # Convert string to bigInteger
    writeln(integer("code", 36));        # Convert string to integer
  end func;
Output:
rosetta
code
60272032366
591458

Sidef

Built-in:

say 60272032366.base(36)    # convert number to string
say Number("rosetta", 36)   # convert string to number

User-defined:

Translation of: Perl
static to = [@|'0'..'9', @|'a'..'z']
static from = Hash(to.pairs.map{@|_}.flip...)

func base_to(n, b) {
    var s = ""
    while (n) {
        s += to[n % b]
        n //= b
    }
    s.reverse
}

func base_from(n, b) {
    var t = 0
    n.each { |c| t = (b*t + from{c}) }
    t
}

say base_from("rosetta", 36)        # string to number
say base_to(60272032366, 36)        # number to string

Slate

26 printString &radix: 16
Integer readFrom: '1A' &radix: 16.

Smalltalk

26 printStringRadix:16 -> '1A'
Integer readFrom:'1A' radix:16 -> 26

2 to:36 do:[:radix |
    'radix %2d: %s\n' printf:{radix . 100 printStringRadix:radix } on:Transcript.
].
Output:
radix  2: 1100100
radix  3: 10201
radix  4: 1210
radix  5: 400
radix  6: 244
radix  7: 202
radix  8: 144
radix  9: 121
radix 10: 100
radix 11: 91
radix 12: 84
radix 13: 79
radix 14: 72
radix 15: 6A
radix 16: 64
radix 17: 5F
radix 18: 5A
radix 19: 55
radix 20: 50
radix 21: 4G
radix 22: 4C
radix 23: 48
radix 24: 44
radix 25: 40
radix 26: 3M
radix 27: 3J
radix 28: 3G
radix 29: 3D
radix 30: 3A
radix 31: 37
radix 32: 34
radix 33: 31
radix 34: 2W
radix 35: 2U
radix 36: 2S

Standard ML

Translation of: Haskell
fun toBase b v = let
  fun toBase' (a, 0) = a
    | toBase' (a, v) = toBase' (v mod b :: a, v div b)
in
  toBase' ([], v)
end

fun fromBase b ds =
  foldl (fn (k, n) => n * b + k) 0 ds

val toAlphaDigits = let
  fun convert n = if n < 10 then chr (n + ord #"0")
                            else chr (n + ord #"a" - 10)
in
  implode o map convert
end

val fromAlphaDigits = let
  fun convert c = if      Char.isDigit c then ord c - ord #"0"
                  else if Char.isUpper c then ord c - ord #"A" + 10
                  else if Char.isLower c then ord c - ord #"a" + 10
                  else raise Match
in
  map convert o explode
end

Example:

val toAlphaDigits = fn : int list -> string
- toAlphaDigits (toBase 16 42);
val it = "2a" : string
- fromBase 16 (fromAlphaDigits "2a");
val it = 42 : int

Swift

Converting integer to string:

println(String(26, radix: 16)) // prints "1a"

Converting string to integer:

import Darwin
func string2int(s: String, radix: Int) -> Int {
  return strtol(s, nil, Int32(radix))
  // there is also strtoul() for UInt, and strtoll() and strtoull() for Int64 and UInt64, respectively
}
println(string2int("1a", 16)) // prints "26"

Tcl

Tcl scan and format commands can convert between decimal, octal and hexadecimal, but this solution can convert between any arbitrary bases.

namespace eval baseconvert {
    variable chars "0123456789abcdefghijklmnopqrstuvwxyz"
    namespace export baseconvert
}
proc baseconvert::dec2base {n b} {
    variable chars
    expr {$n == 0 ? 0
          : "[string trimleft [dec2base [expr {$n/$b}] $b] 0][string index $chars [expr {$n%$b}]]"
    }
}
proc baseconvert::base2dec {n b} {
    variable chars
    set sum 0
    foreach char [split $n ""] {
        set d [string first $char [string range $chars 0 [expr {$b - 1}]]]
        if {$d == -1} {error "invalid base-$b digit '$char' in $n"}
        set sum [expr {$sum * $b + $d}]
    }
    return $sum
}
proc baseconvert::baseconvert {n basefrom baseto} {
    dec2base [base2dec $n $basefrom] $baseto
}

namespace import baseconvert::baseconvert 
baseconvert 12345 10 23 ;# ==> 107h
baseconvert 107h 23 7   ;# ==> 50664
baseconvert 50664 7 10  ;# ==> 12345

Ursala

A function parameterized by the base b performs the conversion in each direction. Folding (=>), iteration (->), and reification (-:) operators among others are helpful.

#import std
#import nat

num_to_string "b" = ||'0'! (-: num digits--letters)*+ @NiX ~&r->l ^|rrPlCrlPX/~& division\"b"

string_to_num "b" = @x =>0 sum^|/(-:@rlXS num digits--letters) product/"b"

This test program performs the conversions in both directions for a selection of numbers in base 8 and base 32.

test_data = <1,2,15,32,100,65536,323498993>

#cast %sLnLUL

tests = 

<
   num_to_string32* test_data,
   string_to_num32* num_to_string32* test_data,
   num_to_string8*  test_data,
   string_to_num8*  num_to_string8* test_data>

output:

<
   <'1','2','f','10','34','2000','9kgcvh'>,
   <1,2,15,32,100,65536,323498993>,
   <'1','2','17','40','144','200000','2322031761'>,
   <1,2,15,32,100,65536,323498993>>

VBA

Private Function to_base(ByVal number As Long, base As Integer) As String
    Dim digits As String, result As String
    Dim i As Integer, digit As Integer
    digits = "0123456789abcdefghijklmnopqrstuvwxyz"
    Do While number > 0
        digit = number Mod base
        result = Mid(digits, digit + 1, 1) & result
        number = number \ base
    Loop
    to_base = result
End Function
Private Function from_base(number As String, base As Integer) As Long
    Dim digits As String, result As Long
    Dim i As Integer
    digits = "0123456789abcdefghijklmnopqrstuvwxyz"
    result = Val(InStr(1, digits, Mid(number, 1, 1), vbTextCompare) - 1)
    For i = 2 To Len(number)
        result = result * base + Val(InStr(1, digits, Mid(number, i, 1), vbTextCompare) - 1)
    Next i
    from_base = result
End Function
Public Sub Non_decimal_radices_Convert()
    Debug.Print "26 decimal in base 16 is: "; to_base(26, 16); ". Conversely, hexadecimal 1a in decimal is: "; from_base("1a", 16)
End Sub
Output:
26 decimal in base 16 is: 1a. Conversely, hexadecimal 1a in decimal is:  26 

Wolframalpha

input box: 1801 decimal to base 16
input box: (99 base 12)+(77 base 8)
This is Mathematica but is worth showing distinctly. Result provides endian choice and other bases typically.

Wren

Library: Wren-fmt

The methods Conv.itoa and Conv.atoi in the above module provide the required functionality.

import "./fmt" for Conv

System.print(Conv.itoa(26, 16))
System.print(Conv.atoi("1a", 16))
Output:
1a
26

XPL0

include c:\cxpl\codes;  \intrinsic 'code' declarations
string 0;               \use zero-terminated string convention

func Num2Str(N, B);     \Convert integer N to a numeric string in base B
int  N, B;
char S(32); int I;
[I:= 31;
S(31):= 0;              \terminate string
repeat  I:= I-1;
        N:= N/B;
        S(I):= rem(0) + (if rem(0)<=9 then ^0 else ^a-10);
until   N=0;
return @S(I);           \BEWARE! very temporary string space
];

func Str2Num(S, B);     \Convert numeric string S in base B to an integer
char S; int B;
int  I, N;
[I:= 0;  N:= 0;
while S(I) do
        [N:= N*B + S(I) - (if S(I)<=^9 then ^0 else ^a-10);  I:= I+1];
return N;
];

[Text(0, Num2Str(0, 10));               CrLf(0);
 Text(0, Num2Str(26, 16));              CrLf(0);
 Text(0, Num2Str($7FFF_FFFF, 2));       CrLf(0);
 IntOut(0, Str2Num("0100", 2));         CrLf(0);
 IntOut(0, Str2Num("1a", 16));          CrLf(0);
 IntOut(0, Str2Num("deadbeef", 16));    CrLf(0);
]

Output:

0
1a
1111111111111111111111111111111
4
26
-559038737

zkl

The toInt(base) and toString(base) methods do this. base is 2..36

(26).toString(16)  //--> "1a"
"1a".toInt(16)    //-->26

In addition, string format is able to convert to a base:

"%x %,.2B".fmt(26,26) //-->"1a 1|1010"