The carry bit is incorrect in my 7 bit adder, I dont know why

[Shibbir Khan]

I have this function and everything works until a and b both equal 1. When that happens the carry bit is going to 2 when its supposed to be only 0 or 1. Is my algorithm wrong for the carry bit
carry_bits |= ((a & mask) & (b & mask)) << 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;
}
}

[Moschops]

carry_bits |= ((a & mask) & (b & mask)) << 1u;

When a is 1, a & mask is 1, or in binary 00000001.
When b is 1, b & mask is 1, or in binary 00000001.

So ((a & mask) & (b & mask)) is00000001 & 00000001, which gives 00000001.

You then apply this:<< 1u which is left shifting 00000001, so you get 00000010, which is binary for 2.

That's why you get 2.