sizeof(string) not including a "\" sign - c

Question

I've been going through strlen and sizeof for strings (char arrays) and I don't quite get one thing.
I have the following code:
int main() {
char str[]="gdb\0eahr";
printf("sizeof=%u\n",sizeof(str));
printf("strlen=%u\n",strlen(str));
return 0;
}
the output of the code is:
sizeof=9
strlen=3
At first I was pretty sure that 2 separate characters \ followed by 0 wouldn't actually act as a NUL (\0) but I managed to figure that it does.
The thing is that I have no idea why sizeof shows 9 and not 10.
Since sizeof counts the amount of used bytes by the data type why doesn't it count the byte for the \?
In a following example:
char str[]="abc";
printf("sizeof=%u\n",sizeof(str));
that would print out "4" because of the NUL value terminating the array so why is \ being not counted?

Answer 1

In a character or string constant, the \ character marks the beginning of an escape sequence, used to represent character values for which there isn't a symbol in the source character set. For example, the escape sequence \n represents the newline character, \b represents the backspace character, \0 represents the zero-valued character (which is also the string terminator), etc.
In the string literal "gdb\0eahr", the escape sequence \0 maps to a single 0-valued character; the actual contents of str are {'g', 'd', 'b', 0, 'e', 'a', 'h', 'r', 0}.

Answer 2

It seems you already have the answer:
At first I was pretty sure that 2 separate characters "\" followed by "0" wouldn't actually act as a NULL "\0" but I managed to figure that it does.
The sequence \0 is an octal escape sequence for the byte 0. So while there are two characters in the code to denote this, it translated to a single byte in the string.
So you have 7 alphabetic characters, a null byte in the middle, and a null byte at the end. That's 9 bytes.

Answer 3

Why should char str[]="gdb\0eahr"; be 10 bytes with sizeof operator? It is 9 bytes because there are 8 string elements + trailing zero.
\0 is only 1 character, not 2. \'s purpose is to escape characters, therefore you might see some of these: \t, \n, \\ and others.
Strlen returns 3 because you have string termination at position str[3].
Single sequence of \ acts as escape character and is not part of string size. If you want to literally use \ in your string, you have to write it twice in sequence like \\, then this is single char of \ printable char.

Answer 4

The C compiler scans text strings as a part of compiling the source code and during the scan any special, escape sequences of characters are turned into a single character. The symbol backslash (\) is used to indicate the start of an escape sequence.
There are several formats for escape sequences. The most basic is a backslash followed by one of several special letters. These two characters are then translated into a single character. Some of these are:
'\n' is turned into a line feed character (0x0A or decimal 10)
'\t' is turned into a tab character (0x09 or decimal 9)
'\r' is turned into a carriage return character (0x0D or decimal 13)
'\\' is turned into a backslash character (0x5C)
This escape sequence idea was used back in the old days so that when a line of text was printed to a teletype machine or printer or a CRT terminal, the programmer could use these and other special command code characters to set where the next character would be printed or to cause the device to do some physical action like ring a bell or feed the paper to the next line.
The escape character also allowed you to embed a double quote (") or a single quote (') into a text string so that you could print text that contain quote marks.
In addition to the above special sequences of backslash followed by a letter there was also a way to specify any character by using a backslash followed by one up to three octal digits (0 through 7). So you could specify a line feed character by either using '\n' or you could use '\12' where 12 is the octal representation of the hexadecimal value A or the decimal value 10.
Then the ability to use a hexadecimal escape sequence was introduced with the backslash followed by the letter x followed by one or more hexadecimal digits. So you can write a line feed character with '\n' or '\12' or '\xa'.
See also Escape sequences in C in Wikipedia.