What does "0b" and "0x" stand for when assigning binary and hexadecimal?

When assigning a binary value and a hexadecimal value directly you can do it as follows (respectively):

uint8_t val1 = 0b10101;
uint8_t val2 = 0xFF;

What does the 0b and 0x mean? Specifically the 0 at the front. Can you have other values instead of 0?

Also as another curious question, what other characters can go in the place of b and x? Is there one for octal as an example?

Solution

Any and all integer literals you can create are summarized in the C++ standard by the grammar production at [lex.icon]

integer-literal:
    binary-literal integer-suffix_opt
    octal-literal integer-suffix_opt
    decimal-literal integer-suffix_opt
    hexadecimal-literal integer-suffix_opt

binary-literal:
    0b binary-digit
    0B binary-digit
    binary-literal '_opt binary-digit

octal-literal:
    0
    octal-literal '_opt octal-digit

decimal-literal:
    nonzero-digit
    decimal-literal '_opt digit

hexadecimal-literal:
    hexadecimal-prefix hexadecimal-digit-sequence

binary-digit:
    0
    1

octal-digit: one of
    0  1  2  3  4  5  6  7

nonzero-digit: one of
    1  2  3  4  5  6  7  8  9

hexadecimal-prefix: one of
    0x  0X

hexadecimal-digit-sequence:
    hexadecimal-digit
    hexadecimal-digit-sequence '_opt hexadecimal-digit

hexadecimal-digit: one of
    0  1  2  3  4  5  6  7  8  9
    a  b  c  d  e  f
    A  B  C  D  E  F

As we can deduce from the grammar, there are four types of integer literals:

Plain decimal, that must begin with a non-zero digit.
Octal, any number with a leading 0 (including a plain 0).
Binary, requiring the prefix 0b or 0B.
Hexadecimal, requiring the prefix 0x or 0X.

The leading 0 for octal numbers can be thought of as the "O" in "Octal". The other prefixes use a leading zero to mark the beginning of a number that should not be interpreted as decimal. "B" is intuitively for "binary", while "X" is for "hexadecimal".