在我的 7 位加法器中，进位不正确，我不知道为什么

我有这个函数，一切正常，直到a和b都等于1。当这种情况发生时，进位位将变为2，而它应该只有0或1。我的进位位算法错了吗
carry_bits |＝（（a&掩码）&（b&mask））<lt；1u；

bool add7bits( unsigned int a, unsigned int b, unsigned int *carry_out, unsigned int     *overflow_out, unsigned int *sum_out)
{
if ( a > ( ( 1u << NUM_BITS ) - 1 ) )
{
    cout << "a value: " << a << " is too large" << endl;
    return false;
}
else if ( b > ( ( 1u << NUM_BITS ) - 1 ) )
{
    cout << "b value: " << b << " is too large" << endl;
    return false;
}
else
{
    unsigned int sum_bits = 0;
    unsigned int carry_bits = 0;
    // Use a mask to access the specific bits of interest
    unsigned int mask = 1u;
    // Handle rightmost bit as a half-adder (no carry input)
    // sum = a ^ b
    // c_out = a & b
    sum_bits |= ( a & mask) ^ ( b & mask);
    // The carry _out_ from this stage sets the carry in for the next,
    // that is, the next higher bit in the carry_bits value
    carry_bits |= ((a & mask) & (b & mask)) << 1u;
    // The remaining bits must be handled with the full adder logic. The last
    // adder in the chain's carry out becomes the carry output return
    // value of this function.
            mask = 1u << 1;
            sum_bits |= ((a & mask) ^ (b & mask) ^ carry_bits);
            carry_bits |= ((a & mask) & (b & mask)) << 1u; 
            mask = 1u << 2;
            sum_bits |= ((a & mask) ^ (b & mask) ^ carry_bits);
            carry_bits |= ((a & mask) & (b & mask)) << 1u;
            mask = 1u << 3;
            sum_bits |= ((a & mask) ^ (b & mask) ^ carry_bits);
            carry_bits |= ((a & mask) & (b & mask)) << 1u;
            mask = 1u << 4;
            sum_bits |= ((a & mask) ^ (b & mask) ^ carry_bits);
            carry_bits |= ((a & mask) & (b & mask)) << 1u;          
            mask = 1u << 5;
            sum_bits |= ((a & mask) ^ (b & mask) ^ carry_bits);
            carry_bits |= ((a & mask) & (b & mask)) << 1u;  
    // Handle bit 6 separately.
    mask = 1u << 6;
    sum_bits = ((a ^b) ^ carry_bits);
    carry_bits |= ((a & mask) & (b & mask)) << 1u;

// Determine the overflow by checking if a and b are both 1.
    bool overflow = false;
    if ((a & mask) & (b & mask))
        overflow = true;
    // ...
    //
 *sum_out = sum_bits;
 *carry_out = carry_bits;
 *overflow_out = overflow;
 cout << a << " + " << b << " = " << *sum_out << endl;;
 cout << "Carry: " << *carry_out << endl;
 cout << "Overflow: " << *overflow_out << endl;
    return true;
}
}