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
<lang Lisp>(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))</lang>
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. <lang ada>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;</lang>
Aime
<lang 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');</lang>
ALGOL 68
Built in or standard distribution routines
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.
<lang algol68>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))</lang> 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.
<lang algol68>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</lang> 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
<lang algolw>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.</lang>
AppleScript
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: <lang AppleScript>-- 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</lang>
- Output:
<lang AppleScript>{{{binary:"11111111", octal:"377", hex:"ff"}, {upperHex:"FF", dgDecimal:"२५५"}}, {{binary:"11110000", octal:"360", hex:"f0"}, {upperHex:"F0", dgDecimal:"२४०"}}}</lang>
AutoHotkey
<lang 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
}</lang> alternate implementation contributed by Laszlo on the ahk forum <lang AutoHotkey>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)
}</lang>
AWK
<lang 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)
}</lang>
BBC BASIC
<lang bbcbasic> 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%</lang>
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
<lang 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)))
);</lang>
C
<lang 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;
}</lang>output
-9223372036854775808 in base 2: -1000000000000000000000000000000000000000000000000000000000000000 383 in base 16: 17f
C#
<lang CSharp> 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();
}
}
} </lang>
C++
<lang cpp>#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;
}</lang>
Caché ObjectScript
<lang cos>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)
}
}</lang>
- 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
<lang lisp>(parse-integer "1a" :radix 16) ; returns multiple values: 26, 2 (write-to-string 26 :base 16) ; also "1A"</lang>
Alternative implementation using FORMAT's ~R directive and #nR reader macro <lang lisp>(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)))</lang>
Yet another approach uses FORMAT's ~R in conjunction with ~V for passing arguments to directives (this assumes input as string) <lang lisp>(defun change-base (number input-base output-base)
(format nil "~vr" output-base (parse-integer number :radix input-base)))</lang>
D
Using Standard Functions
<lang d>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));
}</lang>
- Output:
109517 rosetta code
One Implementation
<lang d>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));
}</lang>
- Output:
'1ABcdxyz???' (base 16) = 109517 Converted only: '1ABcd' rosetta code
Alternative Implementation
<lang d>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;
}</lang>
- Output:
109517
E
<lang e>def stringToInteger := __makeInt def integerToString(i :int, base :int) {
return i.toString(base)
}</lang>
<lang e>? stringToInteger("200", 16)
- value: 512
? integerToString(200, 16)
- value: "c8"</lang>
Elixir
<lang 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</lang>
Erlang
- Output:
12> erlang:list_to_integer("ffff", 17).
78300
13> erlang:integer_to_list(63, 3).
"2100"
Euphoria
<lang 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</lang>
Factor
<lang factor>USE: math.parser
12345 16 >base . "3039" 16 base> .</lang>
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. <lang forth>42 dup 2 base ! . \ 101010 hex . \ 2A decimal</lang>
Many variants of Forth support literals in some bases, such as hex, using a prefix <lang forth>$ff . \ 255</lang>
Fortran
<lang fortran>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</lang>
FreeBASIC
<lang 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</lang>
- 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: <lang funl>$stdout = int( '1a', 16 )</lang>
- Output:
26
Converting from string to integer: <lang funl>$stdout = str( 26, 16 )</lang>
- 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).
<lang go>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)
}
}</lang>
Groovy
Solution: <lang groovy>def radixParse = { s, radix -> Integer.parseInt(s, radix) } def radixFormat = { i, radix -> Integer.toString(i, radix) }</lang>
Test Program: <lang groovy>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)
}</lang>
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:
<lang haskell>Prelude> Numeric.showIntAtBase 16 Char.intToDigit 42 "" "2a" Prelude> fst $ head $ Numeric.readInt 16 Char.isHexDigit Char.digitToInt "2a" 42</lang>
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.
<lang haskell>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</lang>
Example:
<lang haskell>*Main> toAlphaDigits $ toBase 16 $ 42 "2a"
- Main> fromBase 16 $ fromAlphaDigits $ "2a"
42</lang>
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.
<lang haskell>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]</lang>
- Output:
fe FE 11111110 376 fe 11111110 २५४ ٢٥٤
HicEst
<lang 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</lang>
<lang hicest>num=7836416410; txt=zzzzzzz; 7836416410;</lang>
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.
<lang Icon>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</lang>
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: <lang j> 2b100 8b100 10b_100 16b100 36b100 36bzy 4 64 _100 256 1296 1294</lang>
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: <lang j>numerals=: '0123456789abcdefghijklmnopqrstuvwxyz' baseNtoL=: numerals {~ #.inv baseLtoN=: [ #. numerals i. ]</lang> Examples of use: <lang j> 2 baseNtoL 100 101 1100100 1100101
16 baseNtoL 26
1a
36 baseLtoN 'zy'
1294</lang> These may be combined so the conversion performed is derived from the type of argument received. <lang j> base=: baseNtoL :: baseLtoN
16 base 'aa'
170
16 base 170
aa</lang> See also primary verbs Base and Antibase.
Java
for long's: <lang java>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
}</lang>
for BigInteger's: <lang java>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
}</lang>
JavaScript
ES5
<lang javascript>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.</lang>
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. <lang javascript> 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));</lang> Using BigInteger, can convert any base. <lang javascript> // 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();
} </lang>
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.
<lang JavaScript>(() => {
'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)
}));
})();</lang>
- 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
<lang 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];</lang>
Example: <lang jq>(255 | convert(16)),
("ff" | to_i(16)),
("10" | to_i(10))</lang>
- Output:
$jq -M -r -n -f Non-decimal_radices.jq ff 255 10
Julia
<lang julia>
- 26 in base 16 or 2
base(16, 26) base(2, 26)
- Parse to integer
parse(Int, "1a", 16) parse(Int, "101101", 2) </lang>
- Output:
"1a" "11010" 26 45
Kotlin
An approach from first principles rather than using Java library functions:
<lang scala>// 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 = ${convertToDecimal(s, b)}")
}
}</lang>
- Output:
36 base 2 = 100100 -> base 2 = 36 36 base 3 = 1100 -> base 3 = 36 36 base 4 = 210 -> base 4 = 36 36 base 5 = 121 -> base 5 = 36 36 base 6 = 100 -> base 6 = 36 36 base 7 = 51 -> base 7 = 36 36 base 8 = 44 -> base 8 = 36 36 base 9 = 40 -> base 9 = 36 36 base 10 = 36 -> base 10 = 36 36 base 11 = 33 -> base 11 = 36 36 base 12 = 30 -> base 12 = 36 36 base 13 = 2a -> base 13 = 36 36 base 14 = 28 -> base 14 = 36 36 base 15 = 26 -> base 15 = 36 36 base 16 = 24 -> base 16 = 36 36 base 17 = 22 -> base 17 = 36 36 base 18 = 20 -> base 18 = 36 36 base 19 = 1h -> base 19 = 36 36 base 20 = 1g -> base 20 = 36 36 base 21 = 1f -> base 21 = 36 36 base 22 = 1e -> base 22 = 36 36 base 23 = 1d -> base 23 = 36 36 base 24 = 1c -> base 24 = 36 36 base 25 = 1b -> base 25 = 36 36 base 26 = 1a -> base 26 = 36 36 base 27 = 19 -> base 27 = 36 36 base 28 = 18 -> base 28 = 36 36 base 29 = 17 -> base 29 = 36 36 base 30 = 16 -> base 30 = 36 36 base 31 = 15 -> base 31 = 36 36 base 32 = 14 -> base 32 = 36 36 base 33 = 13 -> base 33 = 36 36 base 34 = 12 -> base 34 = 36 36 base 35 = 11 -> base 35 = 36 36 base 36 = 10 -> base 36 = 36
LFE
Converting decimal numbers 26 and 3000 in LFE, using some different mechanisms: <lang lisp> > (: erlang list_to_integer '"1a" 16) 26 > #x1a 26 > (: erlang integer_to_list 26 16) "1A" > (: erlang list_to_integer '"101110111000" 2) 3000 > #b101110111000 3000 > (: erlang integer_to_list 3000 2) "101110111000" </lang>
Liberty BASIC
<lang lb> ' Base Converter v6
global alphanum$ 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$, i, 1), 1) -1
next i
end function
</lang>
Lua
Only had to write 'dec2base' as the reverse is provided by the in-built function 'tonumber' <lang Lua>function dec2base (base, n)
local result, digit = ""
while n > 0 do
digit = n % base
if digit > 9 then digit = string.char(digit + 87) end
n = math.floor(n / base)
result = digit .. result
end
return result
end
local x = dec2base(16, 26) print(x) --> 1a print(tonumber(x, 16)) --> 26</lang>
M2000 Interpreter
<lang M2000 Interpreter> Module Checkit {
k$=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 </lang> Output:
True True
True True
True True
True True
True True
True True
M4
<lang M4>eval(26,16) define(`frombase',`eval(0r$2:$1)') frombase(1a,16)</lang>
Output:
1a 26
Maple
<lang 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:</lang>
- 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[]: <lang Mathematica>IntegerString[26,16] FromDigits["1a", 16])</lang>
Output:
"1a" 26
MATLAB / Octave
Use the built-in functions base2dec() and dec2base(): <lang Matlab>dec2base(26,16) base2dec('1a', 16)</lang>
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. <lang NetRexx>/* 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)
</lang> 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
<lang 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 16 echo "1a".fromBase 16</lang> Output:
1a 26
OCaml
<lang 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"</lang>
# basen_of_int 16 26 ;; - : string = "1a" # int_of_basen 16 "1a" ;; - : int = 26
A real base conversion example:
<lang ocaml>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</lang>
Example:
# to_alpha_digits (to_base 16 42);; - : string = "2a" # from_base 16 (from_alpha_digits "2a");; - : int = 42
PARI/GP
<lang parigp>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
};</lang>
Pascal
<lang 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. </lang> Output:
% ./Convert 1A: 26 26: 1a
Perl
For base 2 and 16, we can do this entirely with language features: <lang perl>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); }</lang>
Small functions will handle arbitrary base conversions for bases 2-36: <lang perl>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);
}
$t;
}</lang>
There are a plethora of modules that perform base conversion.
The core POSIX module includes strtol (and strtoul) which is simple and fast, but only does conversions from a base. On some platforms the function may be limited to 32-bit even with a 64-bit Perl. <lang perl>use POSIX; my ($num, $n_unparsed) = strtol('1a', 16); $n_unparsed == 0 or die "invalid characters found"; print "$num\n"; # prints "26"</lang>
The ntheory module includes functions that will perform base conversion, and is fast. It supports bases up to 36 and bigints.
<lang perl>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"</lang>
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/t/0x/X/# and 0(2..36)
The (s)printf() routine can generate strings in decimal, binary, octal, or hexadecimal, using %d/e/f/g, %b, %o/t, %x/X formats respectively.
The builtin to_number() function has an inbase parameter which defaults to 10 but can be 2..16.
mpz_set_str() and mpfr_set_str() can handle input strings expressed in decimal, binary (0b prefix), or hexadecimal (0x prefix).
mpz_get_str() and mpfr_get_str() can generate output strings in all bases 2..62.
<lang Phix>?{26,0b11010,0o32,0t32,0x1A,0X1a,#1A,0(16)1A} -- displays {26,26,26,26,26,26,26,26}
printf(1,"%d == 0b%b == 0x%x\n",26) -- displays 26 == 0b11010 == 0x1A
?to_number("1a",{},16) -- displays 26</lang>
The following routines can handle all other conversions, in bases 2 to 36.
Note 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.
<lang Phix>-- demo\rosetta\Convert_base.exw
function to_base(integer i, integer base)
integer c
sequence 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 s
end 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 res
end function
?to_base(256,16) ?from_base("100",16)</lang>
- Output:
"100" 256
PHP
PHP has a base_convert() function that directly converts between strings of one base and strings of another base: <lang php>base_convert("26", 10, 16); // returns "1a"</lang>
If you want to convert a string to an integer, the intval() function optionally takes a base argument when given a string: <lang php>intval("1a", 16); // returns 26</lang>
To go the other way around, I guess you can use base_convert() again; I am unaware of a better way: <lang php>base_convert(26, 10, 16); // returns "1a"</lang>
In addition, there are specialized functions for converting certain bases: <lang php>// 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</lang>
PicoLisp
<lang 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))</lang> Output:
"1a" 26 "byw97um9s91dlz68tsi"
PL/I
<lang 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; </lang>
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:
<lang pop11>define number_to_base(n, base);
radix_apply(n, '%p', sprintf, base);
enddefine;</lang>
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:
<lang pop11>define string_in_base_to_number(s, base);
incharitem(stringin(base >< ':' >< s))();
enddefine;</lang>
PureBasic
<lang 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</lang> Sample output:
26 1a
Python
Python: string to number
Converting from string to number is straight forward: <lang python>i = int('1a',16) # returns the integer 26</lang>
Python: number to string
Converting from number to string is harder:
- Recursive
<lang python>digits = "0123456789abcdefghijklmnopqrstuvwxyz" def baseN(num,b):
return (((num == 0) and "0" )
or ( baseN(num // b, b).lstrip("0")
+ digits[num % b]))</lang>
- Iterative
<lang>digits = [[ch] for ch in "0123456789abcdefghijklmnopqrstuvwxyz"]
def baseN(num, b):
if num == 0:
return "0"
result = []
while num != 0:
num, d = divmod(num, b)
result += digits[d]
return .join(result[::-1])</lang>
- Sample run from either
In [1: baseN(26, 16) Out[1]: '1a'
R
<lang 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)
</lang>
Racket
<lang 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)
</lang>
Raku
(formerly Perl 6) <lang perl6>sub from-base(Str $str, Int $base) {
+":$base\<$str>";
}
sub to-base(Real $num, Int $base) {
$num.base($base);
}</lang> 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. ┌─┘
└────────────────────────────────────────────────────────────────────┘
<lang rexx>/*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</lang>
- 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
<lang 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
</lang> 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. <lang ruby>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</lang>
Run BASIC
<lang runbasic>global basCvt$ basCvt$ ="0123456789abcdefghijklmnopqrstuvwxyz"
html "
"for i =1 to 10
RandNum = int(100 * rnd(1)) base = 2 +int(35 * rnd(1))html ""
next i
html "| Decimal | To Base | Num | to Dec |
| ";using("###", RandNum);" | ";using("###", base);" | ";toBase$(base,RandNum);" | ";toDecimal( base, toBase$( base, RandNum));" |
"
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$,i,1),1) -1 next i
end function</lang>
| Decimal | To Base | Num | to Dec |
| 51 | 2 | 110011 | 51 |
| 27 | 10 | 27 | 27 |
| 12 | 18 | c | 12 |
| 90 | 35 | 2k | 90 |
| 99 | 17 | 5e | 99 |
| 99 | 18 | 59 | 99 |
| 55 | 11 | 50 | 55 |
| 56 | 28 | 20 | 56 |
| 71 | 34 | 23 | 71 |
| 61 | 23 | 2f | 61 |
Rust
Rust standard library provides parsing a string in a given radix to all integer types. There is no reverse operation (except for format specifiers for binary, octal, decimal and hexadecimal base).
<lang Rust>fn format_with_radix(mut n: u32, radix: u32) -> String {
assert!(2 <= radix && radix <= 36);
let mut result = String::new();
loop {
result.push(std::char::from_digit(n % radix, radix).unwrap());
n /= radix;
if n == 0 {
break;
}
}
result.chars().rev().collect()
}
- [cfg(test)]
- [test]
fn test() {
for value in 0..100u32 {
for radix in 2..=36 {
let s = format_with_radix(value, radix);
let v = u32::from_str_radix(s.as_str(), radix).unwrap();
assert_eq!(value, v);
}
}
}
fn main() -> Result<(), Box<dyn std::error::Error>> {
println!("{}", format_with_radix(0xdeadbeef, 2));
println!("{}", format_with_radix(0xdeadbeef, 36));
println!("{}", format_with_radix(0xdeadbeef, 16));
println!("{}", u32::from_str_radix("DeadBeef", 16)?);
Ok(())
}</lang>
Scala
<lang Scala>def backToBig(num: String, oldBase: Int): BigInt = BigInt(num, oldBase)
def bigToBase(num: BigInt, newBase: Int): String = num.toString(newBase)</lang>
Seed7
The type integer defines the operator radix and the function integer, which convert to string and vice versa. The type bigInteger defines radix and bigInteger for corresponding purposes.
<lang seed7>$ 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;</lang>
- Output:
rosetta code 60272032366 591458
Sidef
Built-in: <lang ruby>say 60272032366.base(36) # convert number to string say Number("rosetta", 36) # convert string to number</lang>
User-defined:
<lang ruby>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</lang>
Slate
<lang slate>26 printString &radix: 16 Integer readFrom: '1A' &radix: 16.</lang>
Smalltalk
<lang 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.
]. </lang>
- 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
<lang sml>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</lang>
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: <lang swift>println(String(26, radix: 16)) // prints "1a"</lang>
Converting string to integer: <lang swift>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"</lang>
Tcl
Tcl scan and format commands can convert between decimal, octal and hexadecimal, but this solution can convert between any arbitrary bases.
<lang tcl>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</lang>
Ursala
A function parameterized by the base b performs the conversion in each direction. Folding (=>), iteration (->), and reification (-:) operators among others are helpful. <lang Ursala>#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"</lang> This test program performs the conversions in both directions for a selection of numbers in base 8 and base 32. <lang Ursala>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></lang>
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
<lang vb>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</lang>
- 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
The methods Conv.itoa and Conv.atoi in the above module provide the required functionality. <lang ecmascript>import "/fmt" for Conv
System.print(Conv.itoa(26, 16)) System.print(Conv.atoi("1a", 16))</lang>
- Output:
1a 26
XPL0
<lang 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);
]</lang>
Output:
0 1a 1111111111111111111111111111111 4 26 -559038737
zkl
The toInt(base) and toString(base) methods do this. base is 2..36 <lang zkl>(26).toString(16) //--> "1a" "1a".toInt(16) //-->26</lang> In addition, string format is able to convert to a base: <lang zkl>"%x %,.2B".fmt(26,26) //-->"1a 1|1010"</lang>
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