I have been working in C for a couple months now and it has never come to my mind to check where actually the format specifiers implemented/defined in the C language format specifiers like:
%f
%d
%p
%s
#include <stdio.h>
int main(){
printf("%f",7.8);
}
I know these format specifiers are meant to be used with stdio.h but my question is where are they implemented/defined in C?
where are the format specifiers implemented
They are implemented in the specific implementation source code of printf you are using. There are many implementations of prinf and implmentation of C standard library - https://en.wikipedia.org/wiki/C_standard_library#Implementations. You are using one of them.
Some are easier to read - https://github.com/eblot/newlib/blob/master/newlib/libc/stdio/vfprintf.c#L1220 . Some are very hard to comprehend and have been optimized through decades - https://github.com/lattera/glibc/blob/master/stdio-common/vfprintf.c#L293 .
defined in the c language?
printf format specifiers are "defined" - standardized, specified - in the C language standard. The draft of the standard we are using online you can read about them here https://port70.net/~nsz/c/c11/n1570.html#7.21.6.1p1 . But cppreference https://en.cppreference.com/w/c/io/fprintf is friendlier and much better formatted to read than dry standard.