Filling a 2GiB file with 0s in C

I am about to do some data processing in C, and the processing part is working logically, but I am having a strange file problem. I conveniently have 32-bits of numbers to consider, so I need a file of 32-bits of 0s, and then I will change the 0 to 1 if something exists in a finite field.

My question is: What is the best way to make a file with all "0s" in C?

What I am currently doing, seems to make sense but is not working. I currently am doing the following, and it doesn't stop at the 2.4GiB mark. I have no idea what's wrong or if there's a better way.

#include <stdlib.h>
#include <stdio.h>

typedef uint8_t u8;
typedef uint32_t u32;

int main (int argc, char **argv) {

    u32 l_counter32 = 0;
    u8  l_ubyte = 0;
    FILE *f_data; 

    f_data = fopen("file.data", "wb+");
    if (f_data == NULL) {
        printf("file error\n");
        return(0);
    }
    for (l_counter32 = 0; l_counter32 <= 0xfffffffe; l_counter32++) {
        fwrite(&l_ubyte, sizeof(l_ubyte), 1, f_data);   
    }
    fwrite(&l_ubyte, sizeof(l_ubyte), 1, f_data);   //final byte at 0xffffffff
    fclose(f_data);
}

I increment my counter in the loop to be 0xFFFFFFFe, so that it doesn't wrap around and run forever.. I haven't waited for it to stop actually, I just keep checking on the disk via ls -alF and when it's larger than 2.4GiB, I stop it. I checked sizeof(l_ubyte), and it is indeed 8-bits.

I feel that I must be missing some mundane detail.

The faster way to create initalize a file with zeroes (alias \0 null bytes) is using truncate()/ftruncate(). See man page here