# Non-decimal radices/Convert

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.

## 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))`

## 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 ) );    endend.`

## 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 -> Stringon 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 ifend 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 stringend inBaseDigits -- OTHER FUNCTIONS DERIVABLE FROM inBaseDigits ------------------------------- -- inUpperHex :: Int -> Stringon inUpperHex(n)    inBaseDigits("0123456789ABCDEF", n)end inUpperHex -- inDevanagariDecimal :: Int -> Stringon 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    lstend 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 tellend map -- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Scripton mReturn(f)    if class of f is script then        f    else        script            property |λ| : f        end script    end ifend mReturn`
Output:
`{{{binary:"11111111", octal:"377", hex:"ff"}, {upperHex:"FF", dgDecimal:"२५५"}}, {{binary:"11110000", octal:"360", hex:"f0"}, {upperHex:"F0", dgDecimal:"२४०"}}}`

## AutoHotkey

`MsgBox % number2base(200, 16) ; 12MsgBox % 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)
```

## 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++

`#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;}`

## 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();        }     } } `

## 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, "!\$%[email protected]_")
A9XUCDBHK6
USER>Write ##class(Utils.Number).ConvertBase("A9XUCDBHK6", 42, 10, "!\$%[email protected]_")
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)))`

## 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 nothrowin {    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
```

## E

`def stringToInteger := __makeIntdef integerToString(i :int, base :int) {  return i.toString(base)}`
`? stringToInteger("200", 16)# value: 512 ? integerToString(200, 16)# value: "c8"`

## Elixir

`iex(1)> String.to_integer("ffff", 16)65535iex(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 send 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 iend 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 dup2 base !.   \ 101010hex.   \ 2Adecimal`

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 resultEnd 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 resultEnd 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 PrintPrint "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.Listimport 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] -> IntfromBase b ds = foldl' (\n k -> n * b + k) 0 ds toAlphaDigits :: [Int] -> StringtoAlphaDigits = 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.List (unfoldr)import Data.Char (intToDigit) inBaseDigits :: [Char] -> Int -> StringinBaseDigits ds n =  let base = length ds  in reverse \$     unfoldr       (\x ->           (if x > 0              then let (d, r) = quotRem x base                   in Just (ds !! r, d)              else Nothing))       n inLowerHex :: Int -> StringinLowerHex = inBaseDigits "0123456789abcdef" inUpperHex :: Int -> StringinUpperHex = inBaseDigits "0123456789ABCDEF" inBinary :: Int -> StringinBinary = inBaseDigits "01" inOctal :: Int -> StringinOctal = inBaseDigits "01234567" inDevanagariDecimal :: Int -> StringinDevanagariDecimal = inBaseDigits "०१२३४५६७८९" inHinduArabicDecimal :: Int -> StringinHinduArabicDecimal = inBaseDigits "٠١٢٣٤٥٦٧٨٩" toBase :: Int -> Int -> StringtoBase intBase n =  if (intBase < 36) && (intBase > 0)    then inBaseDigits (take intBase (['0' .. '9'] ++ ['a' .. 'z'])) n    else [] 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 representationstatic digitsinitial 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 36bzy4 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 {~ #.invbaseLtoN=: [ #. numerals i. ]`

Examples of use:

`   2 baseNtoL 100 10111001001100101   16 baseNtoL 261a   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 170aa`

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 = 26s = k.toString(16) //gives 1ai = 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 reversefunction 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 reversefunction 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"
}```

## jq

`# Convert the input integer to a string in the specified base (2 to 36 inclusive)def convert(base):  def stream:    recurse(if . > 0 then ./base|floor else empty end) | . % base ;  if . == 0 then "0"  else  [stream] | reverse | .[1:]  | 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  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

` # 26 in base 16 or 2base(16, 26)base(2, 26) # Parse to integerparse(Int, "1a", 16)parse(Int, "101101", 2) `
Output:
```"1a"
"11010"
26
45
```

## 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> #x1a26> (: erlang integer_to_list 26 16)"1A"> (: erlang list_to_integer '"101110111000" 2)3000> #b1011101110003000> (: 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, digit = ""    while n > 0 do        digit = n % base        if digit > 9 then digit = string.char(digit + 87) end        n = math.floor(n / base)        result = digit .. result    end    return resultend local x = dec2base(16, 26)print(x)                    --> 1aprint(tonumber(x, 16))      --> 26`

## 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 stringto_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 chartfind_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 numberfrom_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

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 radixinputs = [ -  '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].toLower    assert c in digits[0 .. <base]    result = result * base + digits.find c   if first == 1: result *= -1 echo 26.toBase 16echo "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 example:
Translation of: Haskell
`let to_base b v =  let rec to_base' a v =    if v = 0 then      a    else      to_base' (v mod b :: a) (v / b)  in    to_base' [] v let from_base b ds =  List.fold_left (fun n k -> n * b + k) 0 ds let to_alpha_digit n =  if n < 10 then    char_of_int (n + int_of_char '0')  else    char_of_int (n + int_of_char 'a' - 10) let to_alpha_digits ds =  let buf = Buffer.create (List.length ds) in    List.iter (fun i -> Buffer.add_char buf (to_alpha_digit i)) ds;    Buffer.contents buf let from_alpha_digit c = match c with    '0'..'9' -> int_of_char c - int_of_char '0'  | 'A'..'Z' -> int_of_char c - int_of_char 'A' + 10  | 'a'..'z' -> int_of_char c - int_of_char 'a' + 10 let from_alpha_digits s =  let result = ref [] in    String.iter (fun c -> result := from_alpha_digit c :: !result) s;    List.rev !result`

Example:

```# to_alpha_digits (to_base 16 42);;
- : string = "2a"
# from_base 16 (from_alpha_digits "2a");;
- : int = 42
```

## 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 = "";  while (\$n) {    \$s .= ('0'..'9','a'..'z')[\$n % \$b];    \$n = int(\$n/\$b);  }  scalar(reverse(\$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.

## 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.

## Phix

`-- demo\rosetta\Convert_base.exwfunction to_base(integer i, integer base)integer csequence s = ""    while i>0 do        c = remainder(i,base)        if c<10 then            c += '0'        else            c += 'a'-10        end if        s = prepend(s,c)        i = floor(i/base)    end while     if length(s) = 0 then        s = "0"    end if     return send function function from_base(string s, integer base)integer res = 0, c    for i=1 to length(s) do        c = s[i]        if c>='0' and c<='9' then            c -= '0'        else            c -= 'a'-10        end if        res = res*base+c    end for    return resend 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 stringdecbin(26); // returns "11010"// converts int to octal stringdecoct(26); // returns "32"// converts int to hex stringdechex(26); // returns "1a"// converts binary string to intbindec("11010"); // returns 26// converts octal string to intoctdec("32"); // returns 26// converts hex string to inthexdec("1a"); // returns 26`

## 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; `

## 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"```

## 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 toDecimalEndProcedure 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

Converting from string to number is easy:

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

Converting from number to string is harder:

`digits = "0123456789abcdefghijklmnopqrstuvwxyz"def baseN(num,b):   return (((num == 0) and  "0" )            or ( baseN(num // b, b).lstrip("0")                 + digits[num % b])) # alternatively:def baseN(num,b):  if num == 0: return "0"  result = ""  while num != 0:    num, d = divmod(num, b)    result += digits[d]  return result[::-1] # reverse k = 26s = baseN(k,16) # returns the string 1a`

## 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) `

## 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. */@@ = @@'<>[]{}()[email protected]#\$%^&*_=|\/;:¢¬≈'            /*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 "  inBif 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──►"maxBerd:  call ser  'illegal digit/numeral  ['?"]  in:  "       xerm:  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 decimal) is:   100   3   2

```100 (base 2)          is          11 (base 3)
```

output   when input used (expressed in base 36) is:   zombieseatingdeadvegetables   10   36

```zombieseatingdeadvegetables (base 36)          is          1038334289300125869792154778345043071467300 (base 10)
```

## Ring

` # Project : Non-decimal radices/Convert see "0 (decimal) -> " + hex(0) + " (base 16)" + nlsee "26 (decimal) -> " + hex(26) + " (base 16)" + nlsee "383 (decimal) -> " + hex(383) + " (base 16)" + nlsee "26 (decimal) -> " + tobase(26, 2) + " (base 2)" + nlsee "383 (decimal) -> " + tobase(383, 2)  + " (base 2)" + nlsee "1a (base 16) -> " + dec("1a") + " (decimal)" + nlsee "1A (base 16) -> " + dec("1A") + " (decimal)" + nlsee "17f (base 16) -> " + dec("17f") + " (decimal)" + nlsee "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)
```

## 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  endend # first three taken from TCLp "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 ihtml "</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 iend 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 iend function`
 Decimal To Base Num to Dec 51 2 110011 51 27 10 27 27 12 18 c 12 90 35 2k 90 99 17 5e 99 99 18 59 99 55 11 50 55 56 28 20 56 71 34 23 71 61 23 2f 61

## Scala

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

## 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 stringsay 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 numbersay base_to(60272032366, 36)        # number to string`

## Slate

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

## 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 convertend 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 Matchin  map convert o explodeend`

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 Darwinfunc 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 ;# ==> 107hbaseconvert 107h 23 7   ;# ==> 50664baseconvert 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 = resultEnd FunctionPrivate 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 = resultEnd FunctionPublic 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.

## XPL0

`include c:\cxpl\codes;  \intrinsic 'code' declarationsstring 0;               \use zero-terminated string convention func Num2Str(N, B);     \Convert integer N to a numeric string in base Bint  N, B;char S(32); int I;[I:= 31;S(31):= 0;              \terminate stringrepeat  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 integerchar 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"`