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Converts numbers to a specified base between 2 and 36, for use in templates such as {{binary}}, {{octal}}, {{hexadecimal}}, etc.

Usage[change source]

local BaseConvert = require('Module:BaseConvert')
BaseConvert.convert({n = 14600926, base = 16}) -- returns 'DECADE'


  • n - (required) the number to be converted, as a string. It may be a number instead, if the input base is 10.
  • base - (required) the base to which the number should be converted. May be between 2 and 36, inclusive.
  • from - the base of the input. Defaults to 10 (or 16 if the input has a leading '0x'). Note that bases other than 10 are not supported if the input has a fractional part.
  • precision - number of digits to be rendered after the radix point. Trailing zeros will be added if needed. If not specified, however many digits are needed will be shown, up to 10.
  • width - minimum number of digits to be rendered before the radix point. Leading zeros will be added if needed.
  • default - Value to return if n is empty or non-numeric. Defaults to the value of n.
  • prefix / suffix - wikitext to add before/after the returned result. Will not be added if n is empty or non-numeric. For example, you might use a prefix of 0x when converting to hex, or a suffix of <sub>8</sub> when converting to octal.

From templates[change source]

In wikimarkup, this module may be called with a function name ntom, e.g.:

Markup Renders as
{{#invoke:BaseConvert|16to10|  FF  }}






All options above are supported, excluding |base=, |from= and |n= which are set by the mandatory options. You may also call convert which is near-identical to the Lua form above.

local p = {}

local digits = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'

function normalizeFullWidthChars(s)
    return mw.ustring.gsub(s, '[!-~]', function(s) 
        return mw.ustring.char(mw.ustring.codepoint(s, 1) - 0xFEE0) 

function _convert(n, base, from, precision, width, default, prefix, suffix)
    n = '' .. n   -- convert to a string
    -- strip off any leading '0x' (unless x is a valid digit in the input base)
    from = tonumber(from)
    if not from or from < 34 then
        local c
        n, c = n:gsub('^(-?)0[Xx]', '%1')
        if c > 0 and not from then from = 16 end

    -- check for a negative sign. Do this while the input is still in string form,
    -- because tonumber doesn't support negative numbers in non-10 bases.
    local sign = ''
    local c
    n, c = n:gsub('^-', '')
    if c > 0 then sign = '-' end
    -- replace any full-width Unicode characters in the string with their ASCII equivalents
    n = normalizeFullWidthChars(n)
    -- handle scientific notation with whitespace around the 'e' e.g. '5 e7'
    n = n:gsub('%s*[eE]%s*', 'e')
    from = from or 10
    local num = tonumber(n, from)
    base = tonumber(base)
    precision = tonumber(precision)
    width = tonumber(width)
    if not num or not base then return default or n end
    local i, f = math.modf(num)

    local t = {}
        local d = (i % base) + 1
        i = math.floor(i / base)
        table.insert(t, 1, digits:sub(d, d))
    until i == 0
    while #t < (width or 0) do
        table.insert(t, 1, '0') 
    local intPart = table.concat(t, '')
    -- compute the fractional part
    local tf = {}
    while f > 0 and #tf < (precision or 10) do
        f = f * base
        i, f = math.modf(f)
        table.insert(tf, digits:sub(i + 1, i + 1))
    -- add trailing zeros if needed
    if precision and #tf < precision then
        for i = 1, precision - #tf do
            table.insert(tf, '0') 

    fracPart = table.concat(tf, '')
    -- remove trailing zeros if not needed
    if not precision then
        fracPart = fracPart:gsub('0*$', '')
    -- add the radix point if needed
    if #fracPart > 0 then
        fracPart = '.' .. fracPart
    return (prefix or '') .. sign .. intPart .. fracPart .. (suffix or '')

function p.convert(frame)
    -- Allow for invocation via #invoke or directly from another module
    local args
    if frame == mw.getCurrentFrame() then
        args = frame.args
        args = frame
    local n = args.n
    local base = args.base
    local from = args.from
    local precision = args.precision
    local width = args.width
    local default = args.default
    local prefix = args.prefix
    local suffix = args.suffix
    return _convert(n, base, from, precision, width, default, prefix, suffix)

setmetatable(p, {
	__index = function(t, k)
		from, base = k:match('^([0-9]+)to([0-9]+)$')
		if not from then return nil end
		return function(frame)
			args = frame.args
    		return _convert(mw.text.trim(args[1]), base, from, args['precision'], args['width'],
    			args['default'], args['prefix'], args['suffix'])

return p