Need advice about coding style

For your questions.

1. What you have specified is a default value if nothing is connected to it. But the value have assigned is only 4 bits long, so if N is anything other than 4, there will be an error.

2. With unsigned type, you have all the arithmetic functions, as you've already done.

r <= a + b;

But in your code, you have extended a by 1 bit correct, but then you also append '1' to the LSB. You need to write:

result_v := ('0' & a) + ('0' & b) + ('0' & ci); -- if you get error about ambiguous types, write unsigned'('0' & ci);

You also have an error in your code. result should be created as

variable result_v : unsigned(N downto 0);

and s should be sliced

s <= result_v(N-1 downto 0);

co <= result_v(N);

3. when you fix the direction errors, result_v will have a length of N+1.