Carry/Borrow in VHDL ALU

Question

I am making a generic N-bit ALU in VHDL. I am having trouble assigning the value for the carry for addition, or borrow for subtraction. I have tried the following:

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL; 

entity alu is
    generic(n: integer :=1); --Default to 1
    port (
        a : in std_logic_vector(n-1 downto 0);
        b : in std_logic_vector(n-1 downto 0);
        op : in std_logic_vector(1 downto 0);
        output : out std_logic_vector(n-1 downto 0);
        carryborrow: out std_logic 
    );
end alu;

architecture Behavioral of alu is
    signal result: std_logic_vector(n downto 0); 
begin
process( a, b, op )
begin
    case op is
    when "00" => 
        result(n) <= '0'; 
        result(n-1 downto 0) <= a and b; --and gate 
        output <= result(n-1 downto 0); 
        carryborrow <= '0'; 
    when "01" => 
        result(n) <= '0'; 
        result(n-1 downto 0) <= a or b; --or gate 
        output <= result(n-1 downto 0); 
        carryborrow <= '0'; 
    when "10" => 
        result(n) <= '0'; 
        result(n-1 downto 0) <= std_logic_vector(signed(a) + signed(b)); --addition
        output <= result(n-1 downto 0); 
        carryborrow <= result(n); 
    when "11" => 
        result(n) <= '0';
        result(n-1 downto 0) <= std_logic_vector(signed(a) - signed(b)); --subtraction
        output <= result(n-1 downto 0); 
        carryborrow <= result(n); 
    when others => 
        NULL; 
    end case; 

end process;

end Behavioral;

This seems to set the carryborrow bit to always be 0. How can I assign it to what it should be without type errors?

Answer 1

There are bugs in your code:

i) You have not taken into account the fact that signals are not updated immediately. Consequently, the following lines will not do as I think you are expecting:

    result(n) <= '0'; 
    result(n-1 downto 0) <= a and b; --and gate 
    output <= result(n-1 downto 0); 

Instead, you need to take the lines driving output and carryborrow outside the combinational process, as you can see below. ii) Assuming you wish this code to be synthesisable, simply putting NULL in your always branch will result in latches being inferred. You need to drive result in the others branch, too.

So, making an assumption about how your carry output is to behave with the and and or operations, this is how I would have written your code:

architecture Behavioral of alu is
    signal result: std_logic_vector(n downto 0); 
begin
process( a, b, op )
begin
    case op is
    when "00" => 
        result <= '0' & (a and b); --and gate 
    when "01" => 
        result <= '0' & (a or b); --or gate 
    when "10" => 
        result <= std_logic_vector(resize(signed(a), n+1) + resize(signed(b), n+1)); --addition
    when "11" => 
        result <= std_logic_vector(resize(signed(a), n+1) - resize(signed(b), n+1)); --subtraction
    when others => 
        result <= (others => 'X');
    end case; 
  end process;

  output <= result(n-1 downto 0); 
  carryborrow <= result(n); 

end Behavioral;

Answer 2

I normally do this:

result <= std_logic_vector(signed(a(n-1) & a) + signed(b(n-1) & b));
result <= std_logic_vector(signed(a(n-1) & a) - signed(b(n-1) & b));

Sign extend and then do the operation to take care of overflow, when the result is one extra bit long.

Answer 3

Hmm, consider this in a 4 bit environment, say a="0101" and b="1001" . Adding them shall give the output="1110" , with NO carry.

However, sign extending with resize(signed(a), n+1) and resize(signed(b), n+1) will set a="00101" and b="11001" and hence result="11110" and carryborrow='1' , which is wrong!

By sign extending vectors a and b , the numeral range has increased to 5 bits, and thus result needs to be 6 bits to be able to hold carry, and we're back to square one. Vectors a and b should only be zero extended, that is '0' & a and '0' & b before adding them to result , and then carryborrow , as MSB(Most Significant Bit) of result , will get the correct value.