Carry Flag in 8-bit Addition

Code

#include <stdio.h>
#include <stdint.h>

void add_with_carry(uint8_t a, uint8_t b, uint8_t* result, uint8_t* carry) {
    // Your logic here
    *result=0,*carry=0;
    for (int i=0;i<8;i++){
        uint8_t first=(a>>i)&1,second=(b>>i)&1;
        (*result) |= ((first ^ second ^ (*carry))<<i);
        (*carry) = (*carry)?((*carry) & (first | second)):(first&second); 
    }
}

int main() {
    uint8_t a, b, result, carry;
    scanf("%hhu %hhu", &a, &b);

    add_with_carry(a, b, &result, &carry);

    printf("%u ", result);
    printf("%u", carry);
    return 0;
}

Solving Approach