[c] How does strcmp() work?

This code is equivalent, shorter, and more readable:

int8_t strcmp (const uint8_t* s1, const uint8_t* s2)
{
    while( (*s1!='\0') && (*s1==*s2) ){
        s1++; 
        s2++;
    }

    return (int8_t)*s1 - (int8_t)*s2;
}

We only need to test for end of s1, because if we reach the end of s2 before end of s1, the loop will terminate (since *s2 != *s1).

The return expression calculates the correct value in every case, provided we are only using 7-bit (pure ASCII) characters. Careful thought is needed to produce correct code for 8-bit characters, because of the risk of integer overflow.