Why are hexadecimal numbers prefixed with 0x?

Question

Why are hexadecimal numbers prefixed as 0x? I understand the usage of the prefix but I don't understand the significance of why 0x was chosen.

Answer 1

Note: I don't know the correct answer, but the below is just my personal speculation!

As has been mentioned a 0 before a number means it's octal:

04524 // octal, leading 0

Imagine needing to come up with a system to denote hexadecimal numbers, and note we're working in a C style environment. How about ending with h like assembly? Unfortunately you can't - it would allow you to make tokens which are valid identifiers (eg. you could name a variable the same thing) which would make for some nasty ambiguities.

8000h // hex
FF00h // oops - valid identifier!  Hex or a variable or type named FF00h?

You can't lead with a character for the same reason:

xFF00 // also valid identifier

Using a hash was probably thrown out because it conflicts with the preprocessor:

#define ...
#FF00 // invalid preprocessor token?

In the end, for whatever reason, they decided to put an x after a leading 0 to denote hexadecimal. It is unambiguous since it still starts with a number character so can't be a valid identifier, and is probably based off the octal convention of a leading 0.

0xFF00 // definitely not an identifier!

Answer 2

The preceding 0 is used to indicate a number in base 2, 8, or 16.

In my opinion, 0x was chosen to indicate hex because 'x' sounds like hex.

Just my opinion, but I think it makes sense.

Good Day!

Answer 3

It's a prefix to indicate the number is in hexadecimal rather than in some other base. The C programming language uses it to tell compiler.

Example:

0x6400 translates to 6*16^3 + 4*16^2 + 0*16^1 +0*16^0 = 25600. When compiler reads 0x6400, It understands the number is hexadecimal with the help of 0x term. Usually we can understand by (6400)₁₆ or (6400)₈ or whatever ..

For binary it would be:

0b00000001

Hope I have helped in some way.

Good day!

Answer 4

Short story: The 0 tells the parser it's dealing with a constant (and not an identifier/reserved word). Something is still needed to specify the number base: the x is an arbitrary choice.

Long story: In the 60's, the prevalent programming number systems were decimal and octal — mainframes had 12, 24 or 36 bits per byte, which is nicely divisible by 3 = log2(8).

The BCPL language used the syntax 8 1234 for octal numbers. When Ken Thompson created B from BCPL, he used the 0 prefix instead. This is great because

1. an integer constant now always consists of a single token,
2. the parser can still tell right away it's got a constant,
3. the parser can immediately tell the base (0 is the same in both bases),
4. it's mathematically sane (00005 == 05), and
5. no precious special characters are needed (as in #123).

When C was created from B, the need for hexadecimal numbers arose (the PDP-11 had 16-bit words) and all of the points above were still valid. Since octals were still needed for other machines, 0x was arbitrarily chosen (00 was probably ruled out as awkward).

C# is a descendant of C, so it inherits the syntax.