parseInt(null, 24) === 23... wait, what?

It's converting null to the string "null" and trying to convert it. For radixes 0 through 23, there are no numerals it can convert, so it returns NaN. At 24, "n", the 14th letter, is added to the numeral system. At 31, "u", the 21st letter, is added and the entire string can be decoded. At 37 on there is no longer any valid numeral set that can be generated and NaN is returned.

js> parseInt(null, 36)
1112745

>>> reduce(lambda x, y: x * 36 + y, [(string.digits + string.lowercase).index(x) for x in 'null'])
1112745

Mozilla tells us:

function parseInt converts its first argument to a string, parses it, and returns an integer or NaN. If not NaN, the returned value will be the decimal integer representation of the first argument taken as a number in the specified radix (base). For example, a radix of 10 indicates to convert from a decimal number, 8 octal, 16 hexadecimal, and so on. For radices above 10, the letters of the alphabet indicate numerals greater than 9. For example, for hexadecimal numbers (base 16), A through F are used.

In the spec, 15.1.2.2/1 tells us that the conversion to string is performed using the built-in ToString, which (as per 9.8) yields "null" (not to be confused with toString, which would yield "[object Window]"!).

So, let's consider parseInt("null", 24).

Of course, this isn't a base-24 numeric string in entirety, but "n" is: it's decimal 23.

Now, parsing stops after the decimal 23 is pulled out, because "u" isn't found in the base-24 system:

If S contains any character that is not a radix-R digit, then let Z be the substring of S consisting of all characters before the first such character; otherwise, let Z be S. [15.1.2.2/11]

(And this is why parseInt(null, 23) (and lower radices) gives you NaN rather than 23: "n" is not in the base-23 system.)

Ignacio Vazquez-Abrams is correct, but lets see exactly how it works...

From 15.1.2.2 parseInt (string , radix):

When the parseInt function is called, the following steps are taken:

• Let inputString be ToString(string).
• Let S be a newly created substring of inputString consisting of the first character that is not a StrWhiteSpaceChar and all characters following that character. (In other words, remove leading white space.)
• Let sign be 1.
• If S is not empty and the first character of S is a minus sign -, let sign be −1.
• If S is not empty and the first character of S is a plus sign + or a minus sign -, then remove the first character from S.
• Let R = ToInt32(radix).
• Let stripPrefix be true.
• If R ≠ 0, then a. If R < 2 or R > 36, then return NaN. b. If R ≠ 16, let stripPrefix be false.
• Else, R = 0 a. Let R = 10.
• If stripPrefix is true, then a. If the length of S is at least 2 and the first two characters of S are either “0x” or “0X”, then remove the first two characters from S and let R = 16.
• If S contains any character that is not a radix-R digit, then let Z be the substring of S consisting of all characters before the first such character; otherwise, let Z be S.
• If Z is empty, return NaN.
• Let mathInt be the mathematical integer value that is represented by Z in radix-R notation, using the letters A-Z and a-z for digits with values 10 through 35. (However, if R is 10 and Z contains more than 20 significant digits, every significant digit after the 20th may be replaced by a 0 digit, at the option of the implementation; and if R is not 2, 4, 8, 10, 16, or 32, then mathInt may be an implementation-dependent approximation to the mathematical integer value that is represented by Z in radix-R notation.)
• Let number be the Number value for mathInt.
• Return sign × number.

NOTE parseInt may interpret only a leading portion of string as an integer value; it ignores any characters that cannot be interpreted as part of the notation of an integer, and no indication is given that any such characters were ignored.

There are two important parts here. I bolded both of them. So first of all, we have to find out what the toString representation of null is. We need to look at Table 13 — ToString Conversions in section 9.8.0 for that information:

Great, so now we know that doing toString(null) internally yields a 'null' string. Great, but how exactly does it handle digits (characters) that aren't valid within the radix provided?

We look above to 15.1.2.2 and we see the following remark:

If S contains any character that is not a radix-R digit, then let Z be the substring of S consisting of all characters before the first such character; otherwise, let Z be S.

That means that we handle all digits PRIOR to the specified radix and ignore everything else.

Basically, doing parseInt(null, 23) is the same thing as parseInt('null', 23). The u causes the two l's to be ignored (even though they ARE part of the radix 23). Therefore, we only can only parse n, making the entire statement synonymous to parseInt('n', 23). :)

Either way, great question!

parseInt( null, 24 ) === 23

Is equivalent to

parseInt( String(null), 24 ) === 23

which is equivalent to

parseInt( "null", 24 ) === 23

The digits for base 24 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, ..., n.

The language spec says

1. If S contains any character that is not a radix-R digit, then let Z be the substring of S consisting of all characters before the first such character; otherwise, let Z be S.

which is the part that ensures that C-style integer literals like 15L parse properly, so the above is equivalent to

parseInt( "n", 24 ) === 23

"n" is the 23-rd letter of the digit list above.

Q.E.D.